Find the radius of convergence, r, of the series. [infinity] n!xn 6 · 13 · 20 · ⋯ · (7n − 1) n = 1 r = find the interval, i, of convergence of the series. (enter your answer using interval notation. )

For a simple sample from a normally distributed population, the degree of freedom and critical value are 24 and X²(L) = 15.6587, X²(R) = 33.1962 respectively. The confidence of interval for estimate is equals to ( 55.8633 , 81.338 ).

We have a simple random sample selected from a population with a normal distribution. The confidence interval

= 80% = 0.80

Sample size, n = 25

standard deviations, s = 65.7

We have to determine value of degree of freedom, critical values. The degrees of freedom represents the number of variables that are free to vary in a calculation, df = n - 1 where n--> numbers of variable. So, in this case degree of freedom = 25 - 1 = 24

Level of significance, α = 1 - 0.80 = 0.20 [tex]\frac{\alpha}{2} = \frac{0.20}{2}[/tex].

= 0.10

Now, critical values are defined as

[tex]{χ^{2} _R} = {χ^{2_{\frac{\alpha}{2}}}}[/tex]

= [tex] { χ²_{\frac{0.20}{2}}}[/tex]

[tex]= { χ^{2} _{0.10}}[/tex] with 24 degree of freedom is equal to 33.1962. Also, left hand critical value, [tex]{χ^{2}_L = { χ^{2} _{(1 - \frac{\alpha}{2})}}}[/tex]

[tex]= { χ²_{0.90}}[/tex] with 24 degree of freedom is 15.6587. The confidence interval estimate formula is [tex]CI = ( \frac{ (n- 1)s²}{χ²_{0.10, n-1}}, \frac{ (n- 1)s²}{χ²_{0.90, n-1}})[/tex]. Plugging alm known values, CI = [tex](\frac{(25 - 1)s²}{χ²_{0.10, 25-1}},\frac{(25 - 1)s²}{χ²_{0.90, 25 -1}})[/tex].

= ( 55.8633 , 81.338 ).

Hence, required value is (55.8633 , 81.338 ).

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Complete question:

Question content area top Part 1 Use the given information to find the number of degrees of freedom, the critical values

and the confidence interval estimate of. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution. White Blood Counts of Women 80% confidence; n = 25, s = 65.7.

Rectangle A’B’C’D’ is the image of rectangle ABCD then 90 degrees rotation about the origin is true

To determine which rotation was done to transform point BBCD to A'B'C'D'

90 degrees rotation about the origin

This transformation would map point ABCD to A'B'C'D" which is the same as A'.

However, this transformation is clockwise, whereas the actual transformation was counterclockwise.

Hence, 90 degrees rotation about the origin, followed by a reflection about the y-axis is correct

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The density of the ball in the air is given as follows:

d = 4 x 10^5 ounces/ft³.

The density is calculated as the division of the mass by the volume of an object, as follows:

d = m/v.

The ball in this problem is spherical with a diameter of 0.05 feet = radius of 0.025 feet, hence the volume is given as follows:

V = 4 x 3.1416 x 0.025³/3

V = 6.545 x 10^-5 ft³.

The ball in the air is inflated, hence the mass is given as follows:

m = 22.93 ounces.

Thus the density of the ball is given as follows:

d = 22.93/(6.545 x 10^-5)

d = 4 x 10^5 ounces/ft³.

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Part(a),

The average rate of change in annual sales between 2001 and 2002 was $14$ million per year.

Part(b),

The average rate of change in annual sales between 2001 and 2004 was a decrease of $3.33$ million per year.

a) To find the rate of change between 2001 and 2002, we need to calculate the difference in sales between those two years and divide it by the number of years:

Rate of change = (Sales in 2002 - Sales in 2001) / (2002 - 2001)

Rate of change = (255 - 241) / 1 = 14 million/year

Therefore, the average rate of change of annual sales between 2001 and 2002 was $14$ million per year.

b) To find the rate of change between 2001 and 2004, we need to calculate the difference in sales between those two years and divide it by the number of years:

Rate of change = (Sales in 2004 - Sales in 2001) / (2004 - 2001)

Rate of change = (231 - 241) / 3 = -3.33 million/year

Therefore, the average rate of change of annual sales between 2001 and 2004 was a decrease of $3.33$ million per year.

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The chemical equation N2 + 3H2 ---> 2NH3 tells us that in order to make two molecules of NH3, we need one molecule of N2 and three molecules of H2.

To figure out how many moles (which is just a way of measuring how much of a substance you have) of H2 we need to react with 14.0 g of N2, we can use the information from the equation.

First, we convert the 14.0 g of N2 to moles (which means we're figuring out how many pieces of N2 we have, because 1 mole = Avogadro's number of particles, or roughly 6.022 x 10^23).

14.0 g N2 x (1 mol N2/28 g N2) = 0.5 mol N2

Then, we use the mole ratio from the equation to figure out how many moles of H2 we need:

0.5 mol N2 x (3 mol H2/1 mol N2) = 1.5 mol H2

So we'd need 1.5 moles of H2 to react completely with 14.0 g of N2.

Answer:

Step-by-step explanation:

To determine if there is a positive linear association between the hours worked and the daily wages of waiters in a restaurant, you can create a scatter plot of the data and look for a pattern.

Once you have the data, you can use a statistical software or a spreadsheet program to create a scatter plot. You can then visually inspect the scatter plot to see if there is a clear pattern of a positive linear association between the two variables.

If there is a positive linear association, the data points on the scatter plot will form a roughly straight line that slopes upwards from left to right. The closer the data points are to the line, the stronger the association.

So, the data table that indicates a positive linear association between the hours worked and the daily wages of waiters in a restaurant is the one where the scatter plot shows a clear upward trend.

The alternative hypothesis is that it is more than 3 grams.

H0: σ ≤ 3

Ha: σ > 3

The null hypothesis (H0) is typically a statement of no effect or no difference, while the alternative hypothesis (Ha) is a statement of the effect or difference that we are trying to detect.

In this case, the null hypothesis is that the standard deviation of the weights of the bags of potato chips is no more than 3 grams, while the alternative hypothesis is that it is more than 3 grams.

H0: σ ≤ 3

Ha: σ > 3

where σ is the population standard deviation.

Step 2 of 3: Determine the appropriate test statistic and critical value(s) for the test.

Since the sample size is greater than 30 and the population standard deviation is unknown, we can use a t-test with (n-1) degrees of freedom. The test statistic is:

t = (s / sqrt(n-1)) / (σ0 / sqrt(n-1))

where s is the sample standard deviation, n is the sample size, and σ0 is the null hypothesis value of the population standard deviation (which is 3 grams in this case).

Under the null hypothesis, the test statistic follows a t-distribution with (n-1) degrees of freedom. To find the critical value(s) for the test at the 0.025 level of significance with 20 degrees of freedom, we need to look up the t-value that has 0.025 probability in the upper tail of the t-distribution with 20 degrees of freedom:

tα = t(0.025,20) ≈ 2.093

Step 3 of 3: Calculate the test statistic and make a decision.

Plugging in the values from the problem, we get:

t =[tex]\frac{(\frac{4.1 }{\sqrt{(21-1)} } )}{\frac{3}{\sqrt{(21-1)} } }[/tex]  ≈ 3.16

The calculated t-value is greater than the critical value, which means that we reject the null hypothesis at the 0.025 level of significance.

In other words, the evidence supports the claim that the standard deviation of the weights of the bags of potato chips is more than 3 grams, and thus the bags do not pass inspection.

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Answer:

The area of the pool is 10*20 = 200 square meters. Let's assume the width of the path is x. Then the dimensions of the entire region would be (10+2x) by (20+2x). The area of the entire region would be (10+2x)*(20+2x) = 400 + 60x + 4x^2. We know that the area of the pool and the path combined is 1200 square meters. So we can set up the equation as follows:

200 + 1200 = 400 + 60x + 4x^2

Simplifying the equation, we get:

4x^2 + 60x - 1000 = 0

Dividing both sides by 4, we get:

x^2 + 15x - 250 = 0

Factoring the equation, we get:

(x + 25)(x - 10) = 0

x = 10 or x = -25

Since the width of the path can't be negative, the width of the path is 10 meters.

Step-by-step explanation:

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In a given linear regression model with given features/predictors, we can compute its coefficients (which multiply corresponding features) by using a mathematical formula called the "ordinary least squares" method. This method finds the best-fit line through the data by minimizing the sum of the squared errors between the predicted values and the actual values.

The resulting coefficients represent the slope of the line for each feature, indicating the strength and direction of the relationship between that feature and the target variable. These coefficients can be used to predict future values of the target variable based on the values of the input features.

Thus, In a given linear regression model with given features/predictors, we can compute its coefficients (which multiply corresponding features) by using the following steps:

1. Organize the data: Arrange the dataset into a matrix (X) containing the features/predictors and a vector (y) containing the target variable.

2. Standardize the data (optional): If the features have different scales, standardize them by subtracting their mean and dividing by their standard deviation.

3. Calculate the coefficient matrix: Compute the coefficients by using the formula:

  β = (X^T * X)^(-1) * X^T * y

  where:
  - β is the coefficient vector (includes coefficients for each feature/predictor)
  - X^T is the transpose of the matrix X
  - (X^T * X)^(-1) is the inverse of the product of X^T and X

4. Interpret the coefficients: The resulting coefficients represent the relationship between each feature/predictor and the target variable. A positive coefficient indicates a positive correlation, while a negative coefficient indicates a negative correlation.

By following these steps, you can compute the coefficients of a linear regression model and understand the relationship between the features/predictors and the target variable.

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The approximate percentage error is 22.1514%.

Formulate:  (427.53−350)÷350

Calculate the sum or difference: 77.53/350

Multiply both the numerator and denominator with the same integer:

7753/35000

Rewrite a fraction as a decimal: 0.221514

Multiply a number to both the numerator and the denominator:

0.221514×100/100

Write as a single fraction: 0.221514×100/100

Calculate the product or quotient: 22.1514/100

Rewrite a fraction with denominator equals 100 to a percentage:

22.1514%

Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.

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Answer:

Standard Form

ax^2 +bx + c = 0

Notice you can already solve for the y-intercept which is (0,4) or y=4

(a) The correlation between x and e can be determined using the formula for the correlation coefficient:

correlation coefficient = covariance(x,e) / (standard deviation of x * standard deviation of e)

Since the covariance between x and e is given as 0.9, and the standard deviation of x is o (given in the question), and the standard deviation of e is o1 (given in the question), we have:

correlation coefficient = 0.9 / (o * o1)

(b) Given y = 3 + xx + e and B1 = 3 and B2 = 1, we can solve for e as:

e = y - B1 - B2x

Substituting the values, we get:

e = y - 3 - x

Using the first 10 observations of x and y, we can calculate the sample correlation between x and e as:

sample correlation coefficient = covariance(x,e) / (standard deviation of x * standard deviation of e)

Using the formula, we can calculate the sample covariance as:

covariance(x,e) = SUM[(xi - x_bar)*(ei - e_bar)] / (n - 1)

where x_bar and e_bar are the sample means of x and e respectively, and n is the sample size (10 in this case).

Similarly, we can calculate the standard deviations of x and e, and then use them to calculate the sample correlation coefficient. We can compare this with the correlation coefficient calculated in part (a).

(c) Plotting y against x and the regression function E(y) = 3 + xx on the same graph, we can see that the data do not fall randomly about the regression function. This suggests that there may be other variables affecting the relationship between y and x.

(d) Estimating the regression model y = Bi + B2x + e by least squares using different sample sizes, we observe that the least squares estimates get closer to the true values as the sample size increases. This is because larger sample sizes provide more information about the relationship between y and x, and reduce the impact of random errors.

(e) To determine if z1 and z2 make good instrumental variables, we need to check their correlation with x and their correlation with e. Using the full set of 500 observations, we can calculate the sample correlations between z1, z2, x, and e. If z1 and z2 are highly correlated with x but uncorrelated with e, then they may be good instrumental variables. Comparing the correlations, we can determine which instrument is better.

(f) Estimating the model y = Bi + B2x + e by instrumental variables using z1 and different sample sizes, we observe that the IV estimates are getting closer to the true values as the sample size increases. This is because larger sample sizes provide more information about the relationship between y and x, and reduce the impact of random errors.

(g) Estimating the model y = Bi + B2x + e by instrumental variables using z2 and different sample sizes, we observe that the IV estimates are getting closer to the true values as the sample size increases. However, the estimates using z1 are generally more precise than those using z2, as z1 has a higher correlation with x.

(h) Estimating the model y = Bi + B2x + e by instrumental variables using both z1 and z2, we observe that the IV estimates are getting closer to the true values as the sample size increases. Using two instruments generally leads to more precise estimation than using one, as it helps to reduce the impact of measurement error in the instrument.

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To calculate the area of regular polygons with sides of length 1, 2, or 3 units, we need to calculate the Perimeter and Apothem using the appropriate formulas and then use the formula A = 1/2 * Perimeter * Apothem to obtain the area.

The area of a regular polygon can be calculated using the formula A = 1/2 * Perimeter * Apothem, where A is the area, Perimeter is the sum of all sides, and Apothem is the distance from the center of the polygon to the midpoint of any side.

For a regular polygon with sides of length 1, the Perimeter would be the product of the number of sides (also called the polygon's order) and the length of each side. Therefore, the Perimeter would be 1 x n, where n is the number of sides. The Apothem can be calculated using the formula Apothem = [tex]$\frac{1}{2}\left(\frac{1}{\tan\left(\frac{\pi}{n}\right)}\right)$[/tex], where π is pi and n is the number of sides. Substituting the values, we get Apothem = [tex]$\frac{1}{2}\left(\frac{1}{\tan\left(\frac{\pi}{n}\right)}\right)$[/tex]. Finally, we can use these values in the formula for area to get the area of the polygon.

Similarly, for a regular polygon with sides of length 2, we would use 2n as the Perimeter and the Apothem would be calculated using the same formula as before. For a polygon with sides of length 3, we would use 3n as the Perimeter and again calculate the Apothem using the same formula.

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Complete question:

What is the method for calculating the area of regular polygons with sides of length 1, 2, and 3 units?

The input x = 6 is mapped to different values, thus, the relation is not a function.

A relationship is a function only if all the inputs are mapped to a single output (this means that each value of the domain is mapped into only one of the values of the range)

Now, the given relation is the following one:

(6, 3), (5, 6), (-1, 1), (6, 9), (8,8)

If you look at the first and the fourth coordinate pairs, you can see that in both cases the inputs are 6.

And the outputs are different, then that input is being mapped to two different values, thus, the relation is not a function.

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Point W has the polar coordinates negative five comma two pi over 3.

We have to given that;

To find the coordinate for the point (- 5, 2π/3).

Now, We can formulate;

Coordinates of W = (- 5, 2π/3).

Thus, The correct point which shows the polar coordinates negative five comma two pi over 3 is,

⇒ Point W

Therefore, Point W has the polar coordinates negative five comma two pi over 3.

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About 4.24% of all samples of 26 of today's women in their 20s have mean heights of at least 63.36 inches.

Since the sample size is 26, we can use the central limit theorem and assume that the distribution of sample means is approximately normal with a mean of 62.8 inches and a standard deviation of 1.65 inches / sqrt(26) = 0.323 inches.

To find the percentage of samples with mean heights of at least 63.36 inches, we need to find the z-score corresponding to this value:

z = (63.36 - 62.8) / 0.323 = 1.74

Using a standard normal distribution table or calculator, we can find that the percentage of samples with z-scores greater than or equal to 1.74 is about 4.24%. Therefore, about 4.24% of all samples of 26 of today's women in their 20s have mean heights of at least 63.36 inches.

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Graph 1 illustrates a shift in the labor supply (LS) curve from LS1 to LS2 that represents an increase in labor supply in the country of Littleland.

In Graph 1, the LS2 curve is positioned to the right of the LS1 curve, indicating an increase in labor supply. This shift could occur due to various factors such as an increase in population, an increase in the number of people entering the labor force, or a decrease in the retirement age. As a result, there is an upward shift in the quantity of labor supplied at each wage level, indicating that more people are willing and able to work at any given wage rate.

Therefore, Graph 1 illustrates an increase in labor supply in the country of Littleland

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The time that it takes for the coconut to land on the net is given as follows:

t = 2.1 seconds.

The quadratic function giving the height of the coconut after t seconds is defined as follows:

h(t) = -4.9t² + S.

In which S represents the height of the canopy.

Ellie uses a pole pruner to release a bunch of coconuts from a canopy 24 meters above the ground, hence the value of S is given as follows:

S = 24.

Thus the function is:

h(t) = -4.9t² + 24.

The coconuts hit the net when h(t) = 1.5, hence the time is obtained as follows:

1.5 = -4.9t² + 24

4.9t² = 22.5

t = sqrt(22.5/4.9)

t = 2.1 seconds.

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The area of the region between the curves y = x^2 and y = x^3 is 1/12 sq units. The correct answer is option a.

To find the area of the region between the curves y = x^2 and y = x^3, we need to integrate the difference between the two curves with respect to x from the point where they intersect.

First, we need to find where the curves intersect by setting them equal to each other:
x^2 = x^3
x^3 - x^2 = 0
x^2(x-1) = 0
x = 0 or x = 1

So the curves intersect at x = 0 and x = 1.

Now, we can set up the integral to find the area between the curves:
A = ∫[0,1] (x^3 - x^2) dx

Evaluating the integral, we get:
A = [x^4/4 - x^3/3] from 0 to 1
A = (1/4 - 1/3) - (0 - 0)
A = 1/12 sq units

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Answer:

3x-5y=0

The standard form for linear equations in two variables is Ax+By=C, so just plug it in.

Answer:

Step-by-step explanation:

Standard form is ax+by=c

[tex]\frac{x}{5} =\frac{y}{3} \\[/tex]      cross multiply to get rid of fractions

3x=5y     now bring the 5y to the other side, by subtracting both sides by 5y

3x-5y=0

The correct option is the last one:

The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.

The theoretical probability is given by.

P  = 100%(number of brown marbles)/(total number)

Then we will get:

P  = 100%*10/40 = 25%

The experimental probability is given by the quotient between the number of times that a brown marble was pulled (13) and the total number of trials, here we have:

E = 100%*13/40

E = 32.5%

So we can see that the experimental probability is larger, and the correct option is the last one.

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Answer:

D

Step-by-step explanation:

Answer:

(7x + 9y) (7x - 9y)

Step-by-step explanation:

   49x² - 81y² = 7²*x² - 9²*y²

                      = (7x)² - (9y)²

[tex]\boxed{\text{\bf Use the identity $ a^2 - b^2 = (a + b)(a-b)$} }[/tex]

Here, 'a' corresponds to 7x and 'b' corresponds to 9y.

                      = (7x + 9y) (7x -9y)

We have evidence to suggest that the standard deviation of the number of fish in a 20-gallon tank is different from twoat the 5% level.

To determine if the standard deviation is different from two at the 5% level, we can perform a hypothesis test. The null hypothesis is that the standard deviation is two, and the alternative hypothesis is that the standard deviation is different from two.

We can use a chi-square test statistic to test this hypothesis. The test statistic is calculated as:

χ² = (n - 1) * s² / σ²

where n is the sample size, s is the sample standard deviation, and σ is the hypothesized population standard deviation.

We can then compare this test statistic to the critical value from the chi-square distribution with n - 1 degrees of freedom at the 5% significance level.

Using the given data, we have:

n = 15

s = 1.256

σ = 2

Plugging these values into the formula, we get:

χ² = (15 - 1) * 1.256² / 2² = 42.891

Using a chi-square distribution table or a calculator, we find that the critical value with 14 degrees of freedom at the 5% level is 23.685.

Since our test statistic (42.891) is greater than the critical value (23.685), we reject the null hypothesis and conclude that the standard deviation is different from two at the 5% level.

Therefore, based on the data provided, we have evidence to suggest that the standard deviation of the number of fish in a 20-gallon tank is different from two.

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Under the equal distribution agreement, X receives $175 less than they would have earned if the earnings were distributed in proportion to their investment.

Profit is defined as the amount gained from selling a product that is greater than the cost price of the product.

If the profits were divided in proportion to the amount invested, then X would receive a fraction of the profits equal to the ratio of their investment to the total investment, and similarly for Y and Z. The total investment is:

$4,500 + $3,500 + $2,000 = $10,000

So the fractions of the profits that X, Y, and Z would receive in proportion to their investments are:

X's fraction = $4,500 / $10,000 = 0.45

Y's fraction = $3,500 / $10,000 = 0.35

Z's fraction = $2,000 / $10,000 = 0.2

Multiplying each fraction by the total profits of $1,500 gives the amount of profits that each person would receive if the profits were divided in proportion to their investments:

X's share = 0.45 * $1,500 = $675

Y's share = 0.35 * $1,500 = $525

Z's share = 0.2 * $1,500 = $300

Since the three partners have agreed to divide the profits equally, each person will receive $1,500 / 3 = $500. The difference between what X receives under the equal division agreement and what they would have received if the profits were divided in proportion to their investment is

$675 - $500 = $175

Therefore, X receives $175 less under the equal division agreement than they would have received if the profits were divided in proportion to their investment.

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Answer:

To find out how many minutes Valeria would practice in 4 weeks, we need to first find out how many minutes she practices per week.

Divide the total number of minutes she practices by the number of weeks she practices:

910 minutes ÷ 5 weeks = 182 minutes per week

Valeria practices 182 minutes per week.

To find out how many minutes she would practice in 4 weeks, we can multiply the minutes per week by the number of weeks:

182 minutes/week x 4 weeks = 728 minutes in 4 weeks

Valeria would practice 728 minutes in 4 weeks.

The volume of the piñata is

1152 cubic in

The volume is solved by breaking the composite shape into two prisms

The volume is solved individually and then added together

Volume of square prism

= area x thickness

= 12 x 12 x 6

= 864 square in

Volume of triangular prism

= area x thickness

= 1/2 x 8 x 12 x 6

= 288 square in

The volume of the piñata

= 864 square in + 288 square in

= 1152 cubic in

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To find 80307 (mod 719) using techniques discussed in Section 8.4, follow these steps:

Step 1: Identify the given numbers:
- The dividend (the number being divided) is 80307.
- The divisor (the number to divide by) is 719.

Step 2: Perform the division operation:
Divide 80307 by 719 to get the quotient and remainder.

80307 ÷ 719 = 111 with a remainder of 678

Step 3: Interpret the remainder:
The remainder is the result of the modulo operation.

So, 80307 (mod 719) = 678.

Your answer is 678.

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Answer: 12

If you are trying to find the length of the long side of the triangle, use this formula: a^2 + b^2 = c^2

So, for you, it'd be 3^2 + 4^2 = 12^2

If it isn't, use this formula: a^2 - b^2 = c^2

EX: 3^2 - 12^2 = 4^2

1.

a.

It will take 8 minutes to fill the bathtub.

b.

The relationship described is linear.

The equation is 20 = 2.5t + 0.

2.

a.

It will take approximately 4.807 hours to have at least 1,000,000 bacteria in the new colony.

b.

The relationship described is exponential,

The equation is Number of bacteria = initial number of bacteria x (reproduction factor)^(time/hour)

We have,

1.

a.

To fill the bathtub, we need 20 gallons of water.

The rate at which the water is being filled is 2.5 gallons per minute.

Using the formula:

time = amount/rate

we get:

time = 20/2.5 = 8 minutes

b.

The relationship described is linear.

The equation relating the variables can be written as:

amount of water = rate x time + initial amount

where the rate is 2.5 gallons per minute, the initial amount is 0 gallons, and the amount of water is 20 gallons.

So, the equation is:

20 = 2.5t + 0

where t is the time in minutes.

2.

a.

The relationship described is exponential.

The equation relating the variables can be written as:

number of bacteria = initial number of bacteria x (reproduction factor)^(time/hour)

where the initial number of bacteria is 1, the reproduction factor is 4, and we need to find the time it takes to reach 1,000,000 bacteria.

So, we have:

1,000,000 = 1 x 4^(time/hour)

Taking the logarithm of both sides, we get:

log(1,000,000) = log(4^(time/hour))

6 = (time/hour) x log(4)

time/hour = 6/log(4)

time = (6/log(4)) x hour

time ≈ 4.807 hours

b.

The relationship described is exponential, and the equation relating the variables is:

Number of bacteria = initial number of bacteria x (reproduction factor)^(time/hour)

where the initial number of bacteria is 1, the reproduction factor is 4, and t is the time in hours.

Thus,

1.

a.

It will take 8 minutes to fill the bathtub.

b.

The relationship described is linear.

The equation is 20 = 2.5t + 0.

2.

a.

It will take approximately 4.807 hours to have at least 1,000,000 bacteria in the new colony.

b.

The relationship described is exponential,

The equation is Number of bacteria = initial number of bacteria x (reproduction factor)^(time/hour)

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