Questions

Exponential Growth

Describe an exponential growth function and describe its graph.

20000 character(s) left
Your answer is too long.

Attachments

There are no attachments

Attach a File

In the “General Growth Formula” shown below, state what A, P, r, and n represent.

A = P(1 + r)ⁿ

4000 character(s) left
Your answer is too long.

Explain three situations that show how the formula in the previous question can be used in the real world.

20000 character(s) left
Your answer is too long.

Attachments

There are no attachments

Attach a File

You are going to invest $200.00 into a savings account with an annual interest rate of 3.75%. Determine how much money you will have earned after 2 1/2 years. State both the growth factor and the amount of money you will have at the end of the 2 1/2 years. Round the answer to the nearest hundredth.

250 character(s) left
Your answer is too long.

If the population of California was 29,760,021 in 2000 and grows by 20% in the decade from 2000 to 2010, state the growth rate and state what the population would be in 2010.

250 character(s) left
Your answer is too long.

Explain the difference between a constant increase situation and an exponential growth situation.

20000 character(s) left
Your answer is too long.

Attachments

There are no attachments

Attach a File

7) What is the general form for constant increase?

250 character(s) left
Your answer is too long.

Growth Factor

What is the general form for exponential growth?

4000 character(s) left
Your answer is too long.

In Example #3 (rabbits) in the link to "Exponential Growth" in the lesson area the problem is: Thirty rabbits are introduced to a secluded area with no predators. Assume that the rabbit population doubles every six months. How many rabbits will be in the area after four (4) years?

Notice that the answer to this problem is 7680 rabbits which is quick growth over a short period of time. This problem demonstrates exponential growth.

Refer to the solution of Example #3 in the content area to solve the next five problems.

After nine (9) years, how many times will the rabbit population have doubled?

250 character(s) left
Your answer is too long.

10)

How many rabbits will there be after 9 years?

250 character(s) left
Your answer is too long.

11)

How many rabbits will there be after 12 years?

250 character(s) left
Your answer is too long.

12)

If the rabbit population TRIPLES in 6 months rather than DOUBLES, how many rabbits would there be after 5 years?

250 character(s) left
Your answer is too long.

13)

Assume the rabbit population in the secluded area doubled EVERY YEAR from 1976 to 2001. How many rabbits would there be in 2001?

250 character(s) left
Your answer is too long.

Constant Increase and Exponential Growth

In the next four questions, an equation is given. Tell whether the graph is linear or exponential. If the graph is exponential, tell if it is growth or decay.

14)

Linear, exponential growth, or exponential decay? y = 2x + 20

250 character(s) left
Your answer is too long.

15)

Linear, exponential growth, or exponential decay? y = 2(1.06)^x

250 character(s) left
Your answer is too long.

16)

Linear, exponential growth, or exponential decay? y = 5x

250 character(s) left
Your answer is too long.

17)

Linear, exponential growth, or exponential decay? y = 3(0.75)^x

250 character(s) left
Your answer is too long.

A large company is making long-range budget plans. This year Smart Mart went from 2400 employees to 2520 employees. The number of employees may be increasing at a constant rate of 120 employees a year OR exponentially by 5% per year. For the next ten problems, refer to the chart below to answer the questions.

18)

Based on the constant increase, how many employees will there be one (1) year from now? (A in the chart)?

250 character(s) left
Your answer is too long.

19)

Based on the exponential growth, how many employees will there be one (1) year from now? (B in the chart)?

250 character(s) left
Your answer is too long.

20)

Based on the constant increase, how many employees will there be two (2) years from now? (C in the chart)?

250 character(s) left
Your answer is too long.

21)

Based on the exponential growth, how many employees will there be two (2) years from now? (D in the chart)?

250 character(s) left
Your answer is too long.

22)

Based on the constant increase, how many employees will there be three (3) years from now? (E in the chart)?

250 character(s) left
Your answer is too long.

23)

Based on the exponential growth, how many employees will there be three (3) years from now? (F in the chart)?

250 character(s) left
Your answer is too long.

24)

Based on the constant increase, how many employees will there be four (4) years from now? (G in the chart)?

250 character(s) left
Your answer is too long.

25)

Based on the exponential growth, how many employees will there be four (4) years from now? (H in the chart)?

250 character(s) left
Your answer is too long.

26)

Based on the constant increase, how many employees will there be five (5) years from now? (I in the chart)?

250 character(s) left
Your answer is too long.

27)

Based on the exponential growth, how many employees will there be five (5) years from now? (J in the chart)?

250 character(s) left
Your answer is too long.

28)

If the number of employees increases at a constant rate, find the projected number of employees 15 years from now.

250 character(s) left
Your answer is too long.

29)

If the number of employees increases exponentially, find the projected number of employees 15 years from now. Round the answer to the nearest whole number.

250 character(s) left
Your answer is too long.

30)

Describe the graph of a function representing exponential decay.

20000 character(s) left
Your answer is too long.

Attachments

There are no attachments

Attach a File

31)

What possible values can the growth factor have in an exponential decay equation?

20000 character(s) left
Your answer is too long.

Attachments

There are no attachments

Attach a File

In Example #1 (town population) in the link to "Exponential Decay" in the lesson area the problem is: A town with a population of 64,500 is losing 3% of its population each year. At this rate, how many people will be left in the town after 15 years?

Notice that the answer to this problem is 40,845 people and shows a sharp decline over a short period of time. This problem demonstrates exponential decay.

Exponential Decay

Refer to the solution of Example #1 under Exponential Decay to solve the next three problems.

32)

What is the population of the town after 1 year?

250 character(s) left
Your answer is too long.

33)

What is the population of the town after 3 years? Round the answer to nearest whole number.

250 character(s) left
Your answer is too long.

34)

If the population of a town declines by 5.2% each year, what would the multiplier be to find the population each year?

250 character(s) left
Your answer is too long.

35)

Thirty-three (33) E. coli bacteria double every 30 minutes. How many bacteria are there after 6 hours?

Hint: consider whether this is a growth or decay problem.

250 character(s) left
Your answer is too long.

36)

Suppose you put $2500 into a savings account that grows with an interest rate of 5.25% and is compounded once each year. How much money will you have after 10 years? Round the answer to the nearest dollar.

250 character(s) left
Your answer is too long.

37)

In Example #1 in the link to "Constant Increase and Exponential Growth," a comparison of constant growth and exponential growth is examined over an 7-day period. Which option is the better choice after 30 days? Explain how you determined the answer.

20000 character(s) left
Your answer is too long.

Attachments

There are no attachments

Attach a File

38) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form.

No offline activities found

0 Hour(s) & 0 Minute(s)

If you are NOT required to complete Offline Activities for this course, please check the box below.

I do not have any Offline Activities for this unit.

Attachments

There are no attachments

Attach a File