If v = 4i and w = 2i + 5i, the angle between the vectors v and w is approximately 47.32 degrees.
To find the angle between two vectors, we can use the dot product formula, which relates the cosine of the angle between the vectors to their dot product and magnitudes. The dot product of two vectors v and w is given by:
v · w = |v| |w| cos(θ)
where |v| and |w| are the magnitudes of the vectors, and theta is the angle between them.
In this case, we are given the vectors v = 4i and w = 2i + 5j. We can compute their dot product as:
v · w = (4i) · (2i + 5j) = 8 + 0 = 8
We can also compute the magnitudes of the vectors as:
|v| = √((4² + 0²)) = 4
|w| = √((2² + 5²)) = √(29)
Substituting these values into the dot product formula, we get:
8 = 4 √(29) cos(θ)
Solving for cos(θ), we get:
cos(θ) = 2 / √(29)
Taking the inverse cosine of both sides, we get:
θ = cos⁻¹(2 / √(29)) = 47.32 degrees
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Mackenzie is going to invest in an account paying an interest rate of 6.5% compounded monthly. How much would Mackenzie need to invest, to the nearest ten dollars, for the value of the account to reach $194,000 in 11 years?
Answer:
Mackenzie would need to invest approximately $91,670, to the nearest ten dollars, for the value of the account to reach $194,000 in 11 years.
Step-by-step explanation:
We can use the formula for compound interest to solve the problem:
A = P(1 + r/n)^(nt)
where:
A = the amount of money in the account after t years
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, we want to find the principal amount P, given that A = $194,000, r = 6.5% = 0.065, n = 12 (compounded monthly), and t = 11 years. Plugging in these values, we get:
194000 = P(1 + 0.065/12)^(12*11)
Simplifying the right side, we get:
194000 = P(1.00541666667)^132
Dividing both sides by (1.00541666667)^132, we get:
P = 194000 / (1.00541666667)^132
P ≈ $91,670.
Therefore, Mackenzie would need to invest approximately $91,670, to the nearest ten dollars, for the value of the account to reach $194,000 in 11 years.
explain pls will give a brainliest answer
By definitions of supplementary angles and by algebra properties, the value of the angle is equal to 118°.
How to find the value of a missing angle
In this problem we get a geometric system formed by a line cutting two parallel lines, from which we find two angles that are supplementary, that is, two angles whose sum equals 180°. Thus, the expression is described below:
(3 · n - 47) + (n + 7) = 180°
Now we proceed to determine to clear variable n by algebra properties:
4 · n - 40 = 180
4 · n = 220
n = 55
And the value of angle ABC is equal to:
m ∠ ABC = 3 · n - 47
m ∠ ABC = 3 · 55 - 47
m ∠ ABC = 118°
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Yulian works at the zoo feeding the animals. He puts water in the elephant habitat at the beginning of the day. This table shows how much water, in gallons, remains at different times during the day.
What is the equation that represents Yulian’s situation, where x represents the time and y represents the amount of water?
Time (h) 2 4 6 8
Water remaining (gal) 43 36 29 22
Enter your answer in the boxes.
y−29= (x− )
The solution is, the equation that represents Yulian’s situation, where x represents the time and y represents the amount of water is
y-29 = -7/2 (x-6).
Here, we have,
The given data is
time (h): 2 4 6 8
gallons: 43 36 29 22
A graph of the data shows a linear relationship.
Therefore in slope-intercept form, let
(y - 29)/(x - 6) = m
where m = the slope of the straight line.
Calculate the slope.
m = (43 - 22)/(2 - 8) = -7/2
Answer: y-29 = -7/2 (x-6)
Hence, The solution is, the equation that represents Yulian’s situation, where x represents the time and y represents the amount of water is
y-29 = -7/2 (x-6).
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Put these mixed numbers into ascending order
3 4/9, 4 1/9, 3 3/9, 3 2/9, 2 5/9
Answer: The mixed numbers in ascending order are:
2 5/9 , 3 2/9 , 3 3/9 , 3 4/9 , 4 1/9
Step-by-step explanation:
To put these mixed numbers into ascending order, we need to convert all of them to improper fractions and then compare them.
3 4/9 = 31/9
4 1/9 = 37/9
3 3/9 = 30/9
3 2/9 = 29/9
2 5/9 = 23/9
so in ascending order (from smallest to largest)
2 5/9 , 3 2/9 , 3 3/9 , 3 4/9 , 4 1/9
If the linear equation 2x+3y=14 is rewritten in function notation as
f(y)=−32y+7,
what is the dependent variable?
If the linear equation 2x+3y=14 is rewritten in function notation as f(y)=−32y+7, the dependent variable is x
In the linear equation 2x+3y=14, we can solve for y by isolating it on one side of the equation:
2x + 3y = 14
3y = -2x + 14
y = (-2/3)x + 14/3
Now, we can write this equation in function notation by replacing y with f(y) and x with the independent variable, usually denoted by 'x'. Therefore, we have:
f(y) = (-2/3)x + 14/3
The function f(y) tells us the value of x for any given value of y. In other words, y is the independent variable, and x is the dependent variable.
Therefore, the dependent variable in the function f(y) = (-2/3)x + 14/3 is x. The value of x is determined by the value of y, which is the input to the function. This means that for any value of y, we can determine the corresponding value of x by plugging in y into the equation and solving for x.
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Form a polynomial f(x) with real coefficients having the given degree and zeros
Degree 4; zeros: 1, multiplicity: 2, 4i
Enter the polynomial. Let a represent the leading coefficient.
1(x)= a(__)
(Type an expression using x as the variable. Use integers or fractions for any numbers in the expression. Simplify your answer.)
The polynomial function of least degree with integer coefficients is: P(x) = a(x³ + 14x² - 31x + 16)
Determining the equation of the polynomialGiven that the properties of the polynomial are
Degree 4; Zeros: 1, multiplicity: 2 Zeros = 4iIf a polynomial has the given zeros 1 with a multiplicity of 2 and another zero at 4i, then its factors can be written as:
P(x) = a(x - 1)²(x - 4i)(x + 4i)
Multiplying out these factors, we get:
P(x) = a(x - 1)²(x + 16)
Expanding the right-hand side, we get:
P(x) = a(x³ + 14x² - 31x + 16)
Therefore, the polynomial function is: P(x) = a(x³ + 14x² - 31x + 16)
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A line passes through the point −6, 9 and has a slope of −2.
Write an equation in slope-intercept form for this line.
The equation of the line in slope-intercept form is y = -2x - 3.
In this case, we know that the line passes through the point (-6,9) and has a slope of -2. Therefore, we can use the point-slope form of the equation to find the equation in slope-intercept form.
Point-slope form:
y - y₁ = m(x - x₁)
Substituting the values we know, we get:
y - 9 = -2(x - (-6))
y = -2x - 3
Therefore, the equation of the line in slope-intercept form is y = -2x - 3.
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The net of a rectangular prism and its dimensions are shown in the diagram. What is the total surface area of the rectangular prism in square inches?
The surface area of the rectangular prism is 216 square inches
What is the surface area of the rectangular prism?From the question, we have the following parameters that can be used in our computation:
10 in by 3 in by 6 in
The surface area of the rectangular prism is calculated as
Surface area = 2 * (Length * Width + Length * Height + Width * Height)
Substitute the known values in the above equation, so, we have the following representation
Area = 2 * (3 * 10 + 3 * 6 + 10 * 6)
Evaluate
Area = 216
Hence, the area is 216 square inches
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Round to the nearest 10th
Answer: What are we finding?
Step-by-step explanation:
The total cost of a meal, including a 20% tip, can be calculated by the formulaT = C + 0.20C. where T is the total cost and O'is the price of the meal including the appropriate tax.
Complete the following statements.
To solve the equation for C, first factor out the common monomial C to rewrite the equation as [Drop Down 1]. Then, divide both sides by the factor [Drop Down 2] to isolate the variable.
To solve the equation for C, first factor out the common monomial C, then rewrite the equation as C(1 + 0.20) = T.
Then, to isolate the variable, divide both sides by the factor (1 + 0.20) or 1.20: C = T/1.20.
How to explain the equationAn equation is essentially a statement that illustrates the variables presented. In this circumstance, it is critical to notice that two or more components are taken into account in order to represent the scenario.
Based on the information, to solve the equation for C, first factor out the common monomial C to rewrite the equation as C(1 + 0.20) = T.
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Select the correct answer.
If no denominator equals zero, which expression is equivalent to 15/x-6 + 7/x+6?
A.
OB.
OC.
OD.
22 +132
²36
22-48
236
22
C.36
22 +48
²36
The expression in the options which is equivalent to the given expression is D. (22x + 48) / (x² - 36).
Given expression is,
[15 / (x - 6)] + [7 / (x + 6)]
Cross multiplying the two fractional expressions,
= [15 (x + 6) + 7 (x - 6)] / [(x - 6) (x + 6)]
= [15x + 90 + 7x - 42] / [x² - 6²]
= (22x + 48) / (x² - 36)
Hence the equivalent expression is D.
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Calculate the producers' surplus for the supply equation at the indicated unit price
p.
HINT [See Example 2.] (Round your answer to the nearest cent.)
p = 150 + e0.01q; p = 170
At a $170 unit price, the producer's excess is $0.
To calculate the producer's surplus at a unit price of p = 170, we need to find the corresponding quantity supplied.
We can start by setting the supply equation equal to the unit price and solving for q:
p = 150 + 0.01q
170 = 150 + 0.01q
20 = 0.01q
q = 2000
So at a unit price of p = 170, the quantity supplied is q = 2000.
To find the producer's surplus, we need to calculate the cost of producing the 2000th unit, which is the marginal cost at this level of production. We can do this by taking the derivative of the supply equation with respect to q:
C(q) = 150q + 0.005q^2
MC(q) = dC/dq = 150 + 0.01q
At q = 2000, the marginal cost is:
MC(2000) = 150 + 0.01(2000) = 170
So the cost of producing the 2000th unit is $170.
The producer's surplus is the difference between the unit price and the marginal cost at the corresponding level of production:
PS = p - MC(q) = 170 - 170 = $0
Therefore, the producer's surplus at a unit price of $170 is $0.
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I need help with this question
One of the potential rational roots of 5x³-7x+11 is ±1, ±11, ±1/5, ±11/5. The correct answer is (B).
Understanding Rational Root TheoremRational Root Theorem states that if a polynomial has integer coefficients, then any rational root of the polynomial must have the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
For the given polynomial:
f(x) = 5x³-7x+11
constant term is 11
leading coefficient is 5.
Therefore, any potential rational roots of f(x) must have the form:
p/q
where p is a factor of 11 and q is a factor of 5.
The factors of 11 are ±1 and ±11, and the factors of 5 are ±1 and ±5. Therefore, the potential rational roots of f(x) are:
±1/1, ±11/1, ±1/5, ±11/5
which simplify to:
±1, ±11, ±1/5, ±11/5
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Let u = - 3i + 2i v = 2i - 2j and w = - 4j Find the specified scalar or vector. 5u(3v - 4w)
If u = - 3i + 2i, v = 2i - 2j and w = - 4j, 5u(3v - 4w) is a scalar quantity with a value of 440.
To evaluate the expression 5u(3v - 4w), we need to first perform the scalar multiplication and then the vector subtraction. We can start by computing the scalar multiplication of 3v - 4w:
3v - 4w = 3(2i - 2j) - 4(-4j) = 6i + 14j
Next, we can perform the scalar multiplication of u and the vector 6i + 14j:
5u(3v - 4w) = 5(-3i + 2j)(6i + 14j)
Expanding the product, we get:
5(-18i² + 36ij + 42ij - 28j²)
Since i² = j² = -1, we can simplify this expression as:
5(18 + 70) = 440
Therefore, 5u(3v - 4w) is a scalar quantity with a value of 440.
The key concept used in this problem is the distributive property of scalar multiplication over vector addition and subtraction. This property allows us to simplify expressions that involve scalar multiplication and vector operations by distributing the scalar to each component of the vector.
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3 The table below shows the thickness of coins.
Coin
quarter
dime
nickel
penny
Thickness
13 millimeters
1 millimeters
20
19 millimeters
20
millimeters
What is the total thickness of a stack that contains 1 dime and 1 penny? Write an
expression and find the answer.
Sow your work.
The total thickness of a stack that contains 1 dime and 1 penny would be 40 millimeters.
How to find the thickness ?If one should find the combined thickness of a collection containing 1 dime and 1 penny, adding both coins' individual thicknesses together is a suitable solution. According to the listed table, a dime's measure is 1 millimeter, while a penny's is 1 7 / 20 millimeters. Consequently, the complete depth of this selection could be calculated as follows:
= Thickness of dime + thickness of penny
= 1 7 / 20 + 1 1 / 2
= 27 / 20 + 3 / 2
= 27 / 20 + 30 / 20
= 57 / 20
= 2 17 / 20 mm
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15 POINTS, HELP!!!!!!!!!! QUICK!!!!
Identify characteristics of the quadratic function and its graph.
The characteristics of the quadratic function and its graph are listed below
Identifying characteristics of the quadratic function and its graph.From the question, we have the following parameters that can be used in our computation:
The graph of the quadratic function
As a general rule
The domain of a quadratic function is the set of all real values
For the range, we have
The graph has a maximum value at y = -1
Also, the values of the function output (y values) decreases
This means that the range is y <= -1
For other key features, we have
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In miss Franco‘s class for every six boys there are a girls write the ratio of boys to girls in simplest form
The ratio of boys to girls in Mrs. Franco's class is 3:2 .
Here, we have,
The Ratio is defined as the comparison of two quantities that have the same units .
In the question ,
it is given that
In Mrs. Franco's class
For every 6 boys there are 4 girls in the class
we have to find the ratio of , boys to girls
the number of boys = 6
the number of girls = 4
So , the ratio can be written as
boys / girls = 6/4
writing the ratio in the simplest form , we get
boys/girls = 3/2
the ratio is 3:2 .
Therefore , The ratio of boys to girls in Mrs. Franco's class is 3:2 .
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complete question:
In Mrs. Franco‘s class for every 64 is there a April right the ratio of boys to girls in simplest form
Robert is preparing to run a marathon. He runs 7 1/5 miles on Saturday and two times that amount on Monday and Wednesday. Robert wants to run a total of 60 miles this week. How many more miles does he need to run?
Answer:
25 miles
Step-by-step explanation:
Robert runs 7 1/5 miles on Saturday. To find out how much he runs on Monday and Wednesday, we can multiply 7 1/5 by 2:
7 1/5 x 2 = 14 2/5
Robert runs 14 2/5 miles on both Monday and Wednesday, so his total distance for the week is:
7 1/5 + 14 2/5 + 14 2/5 = 35 miles
Robert wants to run a total of 60 miles this week, so he needs to run:
60 - 35 = 25 miles
Therefore, Robert needs to run 25 more miles to reach his goal of running 60 miles this week.
To give animals essential minerals and nutrients, farmers and ranchers often have a block of salt (called a "salt-lick") available for their animals to lick.
A rancher is ordering a box of cube-shaped salt licks. The edge lengths of each salt lick are 5/12 -foot. Is the volume of one salt lick greater or less than 1 cubic foot? Explain why or why not.
The volume of one salt lick is 125/1728 feet which is less than one cubic foot.
All the edges of the cube are congruent with each other. Suppose that: The side length of the considered cube is L units. Then, we get:
V = L³ cubic units.
The edge length of the cube is 5/12 feet. Then the volume of the cube will be given as,
V = (5/12)²
V = 125 / 1728 feet
The volume is less than one cubic foot.
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Select the correct answer from each drop-down menu. A transversal t intersects two parallel lines a and b, forms two groups of angles. On top line a, starting from the top left, clockwise, angles are 1, 2, 3, and 4. On below line b, starting from the top left, clockwise, angles are 5, 6, 7, and 8. In the figure, , and both lines are intersected by transversal t. Complete the statements to prove that m∠1 = m∠5. (given) m∠1 + m∠3 = 180° (Linear Pair Theorem) m∠5 + m∠6 = 180° (Linear Pair Theorem) m∠1 + m∠3 = ∠5 + ∠6 ( ) m∠3 = m∠6 ( ) m∠1 = m∠5 (Subtraction Property of Equality)
A transversal t intersects two parallel lines a and b, forming two groups of angles.
On top line a, starting from the top left, clockwise, angles are 1, 2, 3, and 4. On the below line b, starting from the top left, clockwise, angles are 5, 6, 7, and 8.
In the figure, angles 1 and 5 are corresponding angles, and both lines are intersected by transversal t. Complete the statements to prove that m∠1 = m∠5.
(given) m∠1 + m∠3 = 180° (Linear Pair Theorem)
m∠5 + m∠6 = 180° (Linear Pair Theorem)
m∠1 + m∠3 = m∠5 + m∠6 (Vertical Angles Theorem)
m∠3 = m∠6 (Subtraction Property of Equality)
m∠1 = m∠5 (Subtraction Property of Equality)
Thus, this can be concluded regarding the given scenario.
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Um professor precisa organizar 50 alunos em grupo diga quantos alunos haverá em cada grupo se tivemos a seguinte organização
A. Por 2:
B.por:5:
C.por 10:
D.por 25:
E.por 50
3y-1/3=5
*we have to figure out the value of y*
Answer:
To solve for y in the equation:
3y - 1/3 = 5
First, we need to isolate the term containing y by adding 1/3 to both sides of the equation:
3y - 1/3 + 1/3 = 5 + 1/3
Simplifying the left-hand side:
3y = 5 + 1/3
Next, we need to isolate y by dividing both sides of the equation by 3:
3y/3 = (5 + 1/3)/3
Simplifying the right-hand side by finding a common denominator:
3y/3 = (15/3 + 1/3)/3
3y/3 = 16/3
Simplifying the left-hand side:
y = 16/9
Therefore, the solution to the equation 3y - 1/3 = 5 is y = 16/9.
Step-by-step explanation:
What is the equation of this trend line?
K=[]J+[]
The equation of the trend line in slope intercept form is: K = -2J + 28
How to find the equation of a line?The formula for the equation of a line in slope intercept form is expressed in the form:
y = mx + c
where:
m is slope
c is y-intercept
Now, from the given line of best fit, we see that:
At x = 0, y = 28
Thus, c = 28
To get the slope, we will take 2 coordinate points which are:
(2, 24) and (4, 20)
Thus:
m = (20 - 24)/(4 - 2)
m = -2
Thus, the equation is:
K = -2J + 28
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The regular ticketed prices of four items at Grumbell's Clothier are as follows: coat, $139.99;
blouse, $43.99; shoes, $89.99; jeans, $32.99.These four items were placed on sale at 20% off the regular price.
a. Find, correct to the nearest cent, the sale prices of these four items.
b. Describe two different ways to find the sale prices.
The sale prices of the four items are Coat: $111.99, Blouse: $35.19, Shoes: $71.99, Jeans: $26.39 , Using the discount percentage and Using the discount amount are two different ways to find the sale prices.
To find the sale price of each item, we need to multiply the regular price by the discount percentage, which is 20% or 0.2.
Then we subtract this discount amount from the regular price to get the sale price. We can use the following formula:
Sale price = Regular price - Discount amount
Using this formula, we can calculate the sale prices of the four items:
Coat: Sale price = $139.99 - ($139.99 x 0.2) = $111.99
Blouse: Sale price = $43.99 - ($43.99 x 0.2) = $35.19
Shoes: Sale price = $89.99 - ($89.99 x 0.2) = $71.99
Jeans: Sale price = $32.99 - ($32.99 x 0.2) = $26.39
Therefore, the sale prices of the four items are:
Coat: $111.99, Blouse: $35.19, Shoes: $71.99, Jeans: $26.39.
b. There are different ways to find the sale prices. Here are two methods:
Method 1: Using the discount percentage
Multiply the regular price of each item by the discount percentage (20% or 0.2).
Subtract the result from step 1 from the regular price to find the sale price.
Method 2: Using the discount amount
Multiply the regular price of each item by the discount percentage (20% or 0.2) to find the discount amount.
Subtract the discount amount from the regular price to find the sale price.
Both methods will give you the same sale prices, but some people may find one method easier or more intuitive than the other.
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Question #3
The letters A, B, D, and R are each written on an Index card and then put into a hat.
If each letter is drawn randomly, what is the probability of drawing the letters B-R-A-D in that order?
A1/4
B1/2
C
1//24
D 1/30
The overall probability of drawing B-R-A-D in that order is 1/24.
Option C is the correct answer.
We have,
The probability of drawing the letters B-R-A-D in that order is equal to the product of the probabilities of drawing each letter in that order.
Since we are drawing without replacement, the probability of drawing the first letter B is 1/4.
Then, the probability of drawing the second letter R is 1/3
(since one letter has already been drawn and removed from the hat).
Similarly, the probability of drawing the third letter A is 1/2 and the probability of drawing the fourth letter D is 1/1
(since all the other letters have already been drawn and removed).
The overall probability of drawing B-R-A-D in that order.
= (1/4) x (1/3) x (1/2) x (1/1)
= 1/24
Thus,
The overall probability of drawing B-R-A-D in that order is 1/24.
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find the probability that a randomly selected point within the circle falls in the red shaded circle.
Answer:
[tex] \frac{\pi( {4}^{2}) }{\pi( {8}^{2}) } = \frac{16}{64} = \frac{1}{4} = .25[/tex]
The finishing times of two runners for several one-mile races, in minutes, are shown in the box and whisker plots.
Based on the box plots, runner 1 has a faster median time.
true or false?
Answer:
False
Step-by-step explanation:
This is because runner 1's median line falls on 5.6-5.7s while runner 2's falls on 6.4s
(Hopes this helps :) )
Find the sine of ∠Y. Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
Angle Y from the given triangle XYZ is 62° and sine of ∠Y is 60/68.
From the given triangle XYZ, XY=32 and YZ=68.
By using Pythagoras theorem, we get
YZ²=XY²+XZ²
68²=32²+XZ²
XZ²=68²-32²
XZ²=3600
XZ=√3600
XZ=60
We know that, sinθ= Opposite/Hypotenuse
sinY=XZ/YZ
sinY=60/68
sinY=0.8823
Y=61.92
Y≈62°
Therefore, angle Y from the given triangle XYZ is 62° and sine of ∠Y is 60/68.
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Simplify the expression:
5(-6 + 2n) =
Answer:
5(-6 + 2n) can be simplified using the distributive property of multiplication as follows:
5(-6 + 2n) = 5*(-6) + 5*(2n)
= -30 + 10n
Therefore, the simplified expression is -30 + 10n.
The count in a culture of bacteria was 200 after 2 hours and 12,800 after 6 hours.
(a) What is the relative rate of growth of the bacteria population? Express your answer as a percentage. (Round your answer to the nearest whole number.)
(b) What was the initial size of the culture? (Round your answer to the nearest whole number.)
(c) Find a function that models the number of bacteria n(t) after t hours. (Enter your answer in the form n0ert. Round your n0 value to the nearest whole number. Round your r value to two decimal places.)
(d) Find the number of bacteria after 4.5 hours. (Round your answer to the nearest hundred.)
(e) After how many hours will the number of bacteria reach 25,000? (Round your answer to two decimal places.)
a) The relative rate of growth of the bacteria population is approximately 6,300%.
b) The initial size of the culture was approximately 2 bacteria.
c) The function that models the number of bacteria is n(t) = [tex]27e^{(0.88t)[/tex]
d) The number of bacteria after 4.5 hours is approximately 3,106.
e) It takes approximately 5.51 hours for the number of bacteria to reach 25,000.
(a) To find the relative rate of growth of the bacteria population, we can use the formula:
Relative rate of growth = (Final count - Initial count) / Initial count x 100%
Using the values given in the problem, we get:
Relative rate of growth = (12,800 - 200) / 200 x 100% ≈ 6,300%
(b) To find the initial size of the culture, we can use the formula:
Final count = Initial count x e^(relative rate of growth x time)
We can rearrange this formula to solve for the initial count:
Initial count = Final count / e^(relative rate of growth x time)
Using the values given in the problem and solving for the initial count, we get:
Initial count = 200 / [tex]e^{(6300\% \times 2)[/tex] ≈ 2
(c) The function that models the number of bacteria n(t) after t hours is:
n(t) = n₀[tex]e^{(rt)[/tex]
To find the values of n₀ and r, we can use the values given in the problem:
n(2) = 200 = n₀[tex]e^{(2r)[/tex]
n(6) = 12,800 = n₀[tex]e^{(6r)[/tex]
Dividing the second equation by the first equation, we get:
[tex]e^{(4r)[/tex] = 64
Taking the natural logarithm of both sides, we get:
4r = ln(64)
r = ln(64) / 4 ≈ 0.88
Substituting this value of r into the first equation and solving for n₀, we get:
200 = n₀[tex]e^{(0.88 \times 2)[/tex]
n₀ ≈ 27
Therefore, the function that models the number of bacteria is:
n(t) = [tex]27e^{(0.88t)[/tex]
(d) To find the number of bacteria after 4.5 hours, we can use the function we found in part (c):
n(4.5) = 27[tex]e^{(0.88 \times 4.5)[/tex] ≈ 3,106
(e) To find the number of hours it takes for the number of bacteria to reach 25,000, we can use the function we found in part (c):
25,000 = 27[tex]e^ {(0.88t)[/tex]
Dividing both sides by 27 and taking the natural logarithm of both sides, we get:
ln(925.93) = 0.88t
t ≈ 5.51
In summary, we used the formula for relative rate of growth to find the rate of growth of the bacteria population, and used this information to find the initial size of the culture using exponential growth functions.
We found the function that models the number of bacteria, and used it to find the number of bacteria after a given time and the time it takes for the number of bacteria to reach a certain value.
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