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Solve each continuous exponential growth problem.

24. A savings account balance is compounded continuously. If the interest rate is 3% per year and the current balance is $1727.00, what will the balance be 6 years from now?

Answers

Answer 1

Answer:

$2,067.59

Step-by-step explanation:

To calculate the balance of the savings account, we can use the continuous compounding interest formula:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Interest Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]

Given values:

P = $1,727.00r = 3% = 0.03t = 6 years

Substitute the given values into the formula and solve for A:

[tex]\begin{aligned}A&=1727 \cdot e^{0.03 \cdot 6}\\&=1727 \cdot e^{0.18}\\&=1727 \cdot 1.19721736...\\&=2067.59438...\\&=2067.59\end{aligned}[/tex]

Therefore, the balance of the savings account 6 years from now is $2,067.59.


Related Questions

A train travels 70 feet in 1/10th of a second. At this same speed, how many feet will it travel in 3 and 1/2 ( three and one half) seconds?

Answers

Answer:

the train will travel 245 feet in 3 and 1/2 seconds

Step-by-step explanation:

To determine the distance the train will travel in 3 and 1/2 seconds, we can use a proportion based on the given information.

Let's set up the proportion:

70 feet / (1/10 second) = x feet / (3 1/2 seconds)

To solve this proportion, we can first convert the mixed number 3 1/2 to an improper fraction.

3 1/2 = 7/2

Now we can rewrite the proportion:

70 / (1/10) = x / (7/2)

To simplify the proportion, we can multiply the numerator and denominator of the right side by 10/1:

70 / (1/10) = (x * 10) / (7/2)

Simplifying further, we get:

70 * (10/1) = x * (10/7/2)

700 = x * (20/7)

To find x, we can divide both sides of the equation by (20/7):

x = 700 / (20/7)

x = 700 * (7/20)

x = 245 feet

Therefore, at the same speed, the train will travel 245 feet in 3 and 1/2 seconds.

Marianna finds an annuity that pays 8% annual interest, compounded quarterly. She invests in this annuity and contributes $10,000 each quarter for 6 years. How much money will be in her annuity after 6 years? Enter your answer rounded to the nearest hundred dollars.

Answers

The amount of money in Marianna's annuity after 6 years will be approximately $300,516.

To calculate the amount of money in Marianna's annuity after 6 years, we can use the formula for compound interest on an annuity:

A = P * ((1 + r/n)^(n*t) - 1) / (r/n)

Where:

A = the final amount in the annuity

P = the regular contribution (each quarter) = $10,000

r = annual interest rate = 8% = 0.08

n = number of compounding periods per year = 4 (since it's compounded quarterly)

t = number of years = 6

Plugging in the values:

A = 10000 * ((1 + 0.08/4)^(4*6) - 1) / (0.08/4)

Calculating this expression:

A ≈ 10000 * ((1.02)^24 - 1) / 0.02

A ≈ 10000 * (1.601032449136241 - 1) / 0.02

A ≈ 10000 * 0.601032449136241 / 0.02

A ≈ 10000 * 30.05162245681205

A ≈ 300,516.22

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Answer:

304200

Step-by-step explanation:

To find the value of P6, use the savings annuity formula

PN=d((1+r/k)N k−1)r/k.

From the question, we know that r=0.08, d=$10,000, k=4 compounding periods per year, and N=6 years. Substitute these values into the formula gives

P6=$10,000 ((1+0.08/4)6⋅4−1)/(0.08/4).

Simplifying further gives P6=$10,000 ((1.02)24−1)/(0.02) and thus P6=$304,218.62.

Rounding as requested, our answer is 304200.

tion
The graph shows a linear function and an exponential function. Compare and contrast the
two functions. Make sure to use vocabulary words.

Answers

The comparison of the functions is

The linear function has a slope of 50 and it is proportionalThe exponential function has a growth factor of 5/3 and an initial value of 1

How to compare and contrast the two functions

From the question, we have the following parameters that can be used in our computation:

The graph of the two functions

For the linear function, we have

y-intercept = 0

Rate = 50/1 = 50

So, the function is

y = 50x

For the exponential function, we have

y-intercept = 1

Rate = 250/150 = 5/3

So, the function is

y = (5/3)ˣ

Comparing the functions, we have

The linear function has a slope of 50 and it is proportionalThe exponential function has a growth factor of 5/3 and an initial value of 1

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Five less than twice the sum of a number n and twelve

Answers

5-2(n+12) that’s the equation. I hope this helped


a system of equations is shown below
y = 3x - 1
y = - 2x + 4
what is the sum of X and Y in the solution to the system

Answers

Answer:

  3

Step-by-step explanation:

You want the value of (x+y) as determined by the system of equations ...

y = 3x -1y = -2x +4

Solution

We can subtract the second equation from the first to get ...

  (y) -(y) = (3x -1) -(-2x +4)

  0 = 5x -5

  0 = x -1

  1 = x

Using the first equation to find y, we have ...

  y = 3(1) -1 = 2

The sum of x and y is (x +y) = (1 +2) = 3.

Alternate solution

Let t = x+y. This means y = t -x.

Now, the equations become ...

t -x = 3x -1t -x = -2x +4

Adding 4 times the second equation to the first gives ...

  (t -x) +4(t -x) = (3x -1) +4(-2x +4)

  5t -5x = -5x +15

Adding 5x and dividing by 5 gives ...

  t = 3

The sum of x and y is 3.

__

Additional comment

Sometimes you can find the value of the objective function directly, as in the second solution here.

The reason we chose 4 as a multiplier in the alternate solution is that we observed the equations could be written as ...

  t -4x = -1

  t +x = 4

where the variable x has coefficients with a ratio of -4. Using 4 as the multiplier eliminates the x-variable, leaving t — the variable whose value we want.

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PLEASE HELP
I need this done in 15 minutes

Triangle ABC has vertices at A(-5,2), B(1,3), and C(-3,0). Determine the coordinates of the vertices for the image of the pre image is translated 4 units right.
A. A’(-9,2),B’(-3,3), C’(-7,0)
B. A’(-4,6),B’(0,7),C’(1,0)
C. A’(-1,2),B’(5,3),C’(1,0)
D. A’ (-5,-2), B’(-1,-1), C’(-3,-4)

Answers

The coordinates of the vertices for the image of the pre image is translated 4 units right are:

C. A' = (-1,2), B' = (5, 3), C' = (1,0)

How to determine the coordinates of the vertices for the image of the pre image is translated 4 units right?

A geometric transformation involves taking a geometric object as input and producing a new geometric object as output. We have different types of geometric transformations such as translation, rotation, reflection etc.

A translation moves a geometric object a certain distance in a certain direction. Translation to the right means movement in the positive x-direction.

Thus, the coordinates of the vertices for the image of the pre image if it is translated 4 units right can be obtained by adding 4 to x-coordinate values while y-coordinate values remain the same. That is:

A(-5,2) becomes A'(-5+4, 2) = (-1,2)

B(1,3)becomes  B'(1+4, 3) = (5, 3)

C(-3,0) becomes C'(-3+4, 0) = (1,0)

Therefore, the coordinates of the vertices of the image of triangle ABC after it is translated 4 units right are (-1, 2), (5, 3), and (1, 0).

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QUESTION 6 1 POINT
Using the table, what is the average daily balance of the credit card for the August 1 through August 31 billing period?
Round your answer to the nearest dollar.
Provide your answer below:
Day
1
8
16
24
Activity
Payment
Purchase
Purchase
Adjustment Closing Balance
-550
4
+200
+150
850
300
500
650

Answers

Rounded to the nearest dollar, the average daily balance of the credit card for the August 1 through August 31 billing period is $74.

To find the average daily balance of the credit card for the August 1 through August 31 billing period, we need to calculate the sum of the daily balances and divide it by the number of days in the billing period.

Let's calculate the daily balances for each day:

Day 1: Closing Balance = $850

Day 8: Closing Balance = $300

Day 16: Closing Balance = $500

Day 24: Closing Balance = $650

To calculate the daily balances, we need to consider the activities that occurred on each day.

On Day 1, there was no activity recorded, so the closing balance remains at $850.

On Day 8, a payment of $550 was made. Therefore, the closing balance is $850 - $550 = $300.

On Day 16, a purchase of $200 was made. Therefore, the closing balance is $300 + $200 = $500.

On Day 24, a purchase of $150 was made and an adjustment of $4 was applied. Therefore, the closing balance is $500 + $150 - $4 = $650.

Now, let's calculate the average daily balance:

Sum of daily balances = $850 + $300 + $500 + $650 = $2300

Number of days in the billing period = 31

Average daily balance = Sum of daily balances / Number of days = $2300 / 31 ≈ $74.19

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The functions f(x) = x^2 – 3 and g(x) = –x^2 + 2 are shown on the graph.
The graph shows f of x equals x squared minus 3, which is an upward-opening parabola with a vertex at 0 commas negative 3 and a point at negative 1 comma negative 2, and a point at 1 comma negative 2. The graph also shows g of x, which is a downward opening parabola with a vertex at 0 commas 2 and a point at negative 1 comma 1, and a point at 1 comma 1.


Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?


y ≤ x^2 – 3

y > –x^2 + 2

Answers

The solution set to the given system of inequalities is represented by the shaded region under the curve of f(x) = x^2 – 3 (including the points on the curve) and above the curve of g(x) = –x^2 + 2 (excluding the points on the curve). The overlapping region between these shaded areas represents the solution set to the system.

To graph the solution set to the system of inequalities y ≤ x^2 – 3 and y > –x^2 + 2, we can modify the graphs of f(x) = x^2 – 3 and g(x) = –x^2 + 2 accordingly. Here's how:

For the inequality y ≤ x^2 – 3:

The original graph of f(x) = x^2 – 3 is an upward-opening parabola with a vertex at (0, -3).

To graph y ≤ x^2 – 3, we need to shade the region below or on the parabola. This includes all points on the parabola itself.

Therefore, we shade the area under the curve of the original graph of f(x) and include the points on the curve.

For the inequality y > –x^2 + 2:

The original graph of g(x) = –x^2 + 2 is a downward-opening parabola with a vertex at (0, 2).

To graph y > –x^2 + 2, we need to shade the region above the parabola. This excludes all points on the parabola itself.

Therefore, we shade the area above the curve of the original graph of g(x) but exclude the points on the curve.

By modifying the graphs of f(x) and g(x) according to these shading instructions, we can graphically represent the solution set to the system of inequalities.

The solution set can be identified by observing the overlapping region or the intersection between the shaded area under the curve of f(x) and the shaded area above the curve of g(x). The points within this overlapping region satisfy both inequalities simultaneously.

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Using the image below, find the missing part indicated by the question mark.
(3 separate questions)

Answers

The missing part indicated in the figures are ? = 12, TX = 9 and x = 20

How to find the missing part indicated in the figures

Figure a

The missing part can be calculated using the following equation

?/(11 - 5) = 22/11

Evaluate the difference

?/6 = 22/11

So, we have

? = 6 * 22/11

Evaluate the expression

? = 12

Figure b

The missing part can be calculated using the following equation

TX/3 = 6/2

So, we have

TX = 3 * 6/2

Evaluate

TX = 9

Figure c

The value of x can be calculated using the following equation

1/4x + 6 = 2x - 29

So, we have

x + 24 = 8x - 116

Evaluate

-7x = -140

Divide

x = 20

Hence, the value of x is 20

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PLEASE HELP (60)POINTS

Answers

The points (2, 1), (1, 0), (2, 1), (4, 2), and (8, 3) will be plotted on the graph accordingly. The x-coordinate represents the value from the domain, and the y-coordinate represents the corresponding value obtained by evaluating the equation

To plot the points on the graph for the equation y = log2x, we will substitute the given values from the domain (2, 1, 2, 4, 8) into the equation and calculate the corresponding y-values.

For x = 2, y = log2(2) = 1. The point (2, 1) represents this on the graph.

For x = 1, y = log2(1) = 0. The point (1, 0) represents this on the graph.

For x = 2, y = log2(2) = 1. The point (2, 1) represents this on the graph.

For x = 4, y = log2(4) = 2. The point (4, 2) represents this on the graph.

For x = 8, y = log2(8) = 3. The point (8, 3) represents this on the graph.

Now, we can plot these points on the graph. The x-axis will range from 0 to 10, and the y-axis will range from -1 to 4 to accommodate the points we have calculated.

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Which table matches the equation for y = 3/2x-3

Answers

Answer: I think it's H, if it isn't and you get a second try it should be N

Step-by-step explanation: Both H and N start with 0/-3 except F which means F is wrong. Maybe you should wait for a better answer...but it shouldn't be F

You just completed your math course and you want to calculate your overall grade. You know that tests are weighted 15%, quizzes 10%. projects 35%, participation 35%, and the final exam 5%. What is your overall grade if you scored the following in each category?

Answers

Your overall grade, rounded to the nearest hundredth, is approximately 86.35%.

To calculate your overall grade, we need to assign weights to each category and then calculate the weighted average based on your scores.

Let's assume your scores in each category are as follows:

Tests: 85%

Quizzes: 90%

Projects: 92%

Participation: 80%

Final Exam: 88%

Now, let's calculate the weighted average:

Tests: 15% weight × 85% score = 12.75

Quizzes: 10% weight × 90% score = 9.00

Projects: 35% weight × 92% score = 32.20

Participation: 35% weight × 80% score = 28.00

Final Exam: 5% weight × 88% score = 4.40

Overall Grade = Sum of weighted scores / Total weight

Overall Grade = (12.75 + 9.00 + 32.20 + 28.00 + 4.40) / 100

Overall Grade ≈ 86.35%

Therefore, your overall grade, rounded to the nearest hundredth, is approximately 86.35%.

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Mark’s cost does not vary directly with time spent talking because

Answers

Mark's cost does not vary directly with time spent talking, it indicates the presence of other factors, such as pricing structure, additional services, peak hours, bundled packages, or promotions, that influence the overall cost. These factors can lead to non-linear cost variations and a lack of direct proportionality between the cost and time spent talking.

If Mark's cost does not vary directly with the time spent talking, it means that there is not a simple proportional relationship between the two variables. In other words, doubling the time spent talking does not necessarily result in doubling the cost. This indicates that there are other factors influencing Mark's cost besides just the time spent talking.

There can be several reasons why Mark's cost does not vary directly with time spent talking:

Pricing structure: Mark's cost may be determined by a pricing structure that includes fixed fees or additional charges based on certain conditions. For example, there might be a base rate for a certain duration of talk time, and any additional time may be billed at a different rate.

Additional services: Mark's cost might include additional services or features that are not solely dependent on talk time. For instance, there could be charges for international calling, call forwarding, or other value-added services.

Peak hours or special rates: Mark's cost might be affected by peak hours or special rates. Some service providers offer different pricing during certain times of the day or specific days of the week. This could result in non-linear cost variations with respect to time spent talking.

Bundled packages: Mark's cost might be part of a bundled package that includes other services like internet or television. In such cases, the overall cost may be influenced by factors other than talk time.

Promotions or discounts: Mark's cost may be subject to promotional offers or discounts that are not directly related to the time spent talking.

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write inequality shown y=-11/7x-4

Answers

Answer:The inequality represented by the equation y = -11/7x - 4 can be written as:

y ≤ -11/7x - 4

This represents a less than or equal to inequality, indicating that the values of y are less than or equal to the expression -11/7x - 4.

Step-by-step explanation: .

Determine whether 548 is greater than or less than 373. Then write the expression showing this using < or >.

Answers

Answer:

548 > 373

Step-by-step explanation:

548 is greater than 373 because when we compare the digits from left to right, we find that the first digit of 548 (5) is greater than the first digit of 373 (3). Therefore, we can conclude that 548 is greater than 373.

The ">" symbol is used to represent "greater than" in mathematical comparisons.

Hope this helps!

Find the length of side X in simple radical form with a rational denominator

Answers

The length of side X in simple radical form with a rational denominator is 25/√3.

What is a 30-60-90 triangle?

In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):

Adjacent side = 5/√3

Hypotenuse, x = 5 × 5/√3

Hypotenuse, x = 25/√3.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

write the inequality shown -4x+y=-3

Answers

The inequality corresponding to the equation -4x + y = -3 is either y > 4x - 3 or y < 4x - 3, depending on the relationship between 4x - 3 and 0.

To write the inequality represented by the equation -4x + y = -3, we first need to manipulate the equation to express y in terms of x.

Starting with -4x + y = -3, we isolate y by adding 4x to both sides:

y = 4x - 3

Now we have y expressed in terms of x. To form the inequality, we consider the relationship between x and y. The inequality depends on whether the expression 4x - 3 is greater than or less than 0.

If 4x - 3 is greater than 0, then y is greater than 0, and we can write the inequality as:

y > 4x - 3

If 4x - 3 is less than 0, then y is less than 0, and we can write the inequality as:

y < 4x - 3

The inequality represents a region in the coordinate plane where the y-values are either greater than or less than the expression 4x - 3, depending on the direction of the inequality sign.

For example, if we choose a point (x, y) in the region above the line y = 4x - 3, where y is greater than 4x - 3, the inequality y > 4x - 3 will hold true. On the other hand, if we choose a point below the line, where y is less than 4x - 3, the inequality y < 4x - 3 will be satisfied.

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1. A company has $6582 to give out in bonuses. An amount is to be given out equally to each of the 32 employees.
(a) A manager, Jake, reasoned that since 32 goes into 64 twice, each employee will get about $2000. Is his estimate correct? Why or why not?
(b) How much will each employee receive, rounded to the nearest whole dollar? Leave the remainder undivided. Show your work.
Answer:

Answers

Answer:

A) His estimate is incorrect, since he has increased a figure to the amount that each employee would receive.

B) Rounded to the nearest dollar, each employee would receive $ 209.

Step-by-step explanation:

Since a company has $ 6582 to give out in bonuses, and an amount is to be given out equally to each of the 32 employees, and A) a manager, Jake reasoned that since 32 goes into 64 twice, each employee will get about $ 2000 , to determine if his estimate is correct, and B) determine how much will each employee receive, rounded to the nearest whole dollar, the following calculations must be performed:

A)

2000 x 32 = 64000

200 x 32 = 6400

Therefore, his estimate is incorrect, since he has increased a figure to the amount that each employee would receive.

B)

6582/32 = X

208.68 = X

Therefore, rounded to the nearest dollar, each employee would receive $ 209.

HELP PLEASEEE I NEED IMMEDIATELY

Answers

There are like 4 people watching this question...

Answer:

1335.6

Step-by-step explanation:

volume = pir^2 h = (3.14)(6)^2(15) = (3.14)(36)(15) = (47.1)(36) = 1,335.6

The volume of the tank is 1695.60 ft³.

What is the volume of the tank?

A cylinder is a three-dimensional object. It is a prism with a circular base. The volume is the amount of space in an object.

Volume of a cylinder = πr²h

Where:

π = 3.14 h = height = 15r = radius = 6

= 3.14 x 6² x 15 = 1695.60 ft³

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How many 20kobo make up #20

Answers

Answer:

100

Step-by-step explanation:

#20 naira - 20 * 100

= 2000kobo

2000/20

100

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PLEASE HELP 50 POINTS!!
The sum of two consecutive numbers is 157. This equation, where n is the first number, represents the situation:
2n + 1 = 157.
What is the first number?
A. 77
B. 78
C. 79
D. 80

Answers

If a supposed number is n (say) then the consecutive number is n+1
If u add them n+(n+1) you get 157
So,
n+n+1=157
2n=156
n=78
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U-shaped valleys If the price per unit decreases because of competition but the cost structure remains the same A.The breakeven point rises B.The degree of combined leverage declines C.The degree of financial leverage declines) D.All of these JavaScript-Which of the following will display the value of birthday in the document, formatted as Wed Feb 08 2017?birthday = document.getElementById(toDateString());document.write(birthday.toDateString());today = document.write(birthday.toDateString());document.write.birthday.toDateString()); Surgery rooms should be cleaned daily whether they need it or not.a. trueb. false 9.2 Employing Passive-Voice Verbs (L.O. 3) YOUR TASK Revise the following sentences to present thebad news with passive-voice verbs.Chapter9 NegativeMessagesa. Because management now requires more stringent security, we are postponing indefinitely requests for company tours.b. WecannotofferfreeshippingafterJanuary1.Actnow!c. Our retail stores will no longer be accepting credit cards for purchases under $5.d. As manager, I cannot grant you the three-week vacation period you request because others have already reserved that period.e. We do not examine patients until we have verified their insurance coverage.f. Your car rental insurance coverage does not cover large SUVs.g. Company policy prevents us from offering health and dental benefits until employees have been on the job for 12 months. a clause in a contract that automatically increases wages I account for increases in the price level is a. a cola b. the gdp deflation c. the PCs index d. the real rate of interest Fargo Memorial Hospital has annual net patient service revenues of $14,400,000. It has two major third-party payers, plus some of its patients are self-payers. The hospital's patient accounts manager esti- mates that 10 percent of the hospital's paying patients (its self-payers) pay on Day 30, 60 percent pay on Day 60 (Payer A), and 30 percent Chapter 16: Current Asset Management and Financing. 603 pay on Day 90. a. What is Fargo's average collection period?b. What is the firm's current receivables balance? c. What would be the firm's new receivables balance if a newly pro- posed electronic claims system resulted in collecting from third- party payers in 45 and 75 days, instead of in 60 and 90 days? sketch the graph of the function f defined for all t by the given formula, and determine whether it is periodic. If so, find its smallest period. is there a dimension of industry structure that porters model appears to omit?