Honors Advanced Algebra Name: ______

Exponential growth and decay, half-life, compound interest.

Growth and Decay Function

Half-life

Interest Compounded Continually

  1. A coin had a value of $257.00 in 1995. Its value has been increasing at 9% per year.
  2. What is the total value after5 years?
  3. When will the coin be worth $600.?
  1. Gina deposited $2200 in an account that pays 4% interest compounded quarterly.
  2. What will the balance be in 2 years?
  3. When will the account have approximately $2946.00?
  1. The Garcias have $15,000 in a savings account. The bank pays 2.5% interest on savings account, compounded monthly.
  2. Find the total balance after six years.
  3. In what year will the account double?
  4. In what year will the account triple?
  1. If the current average cost to attend college is $60,000.00, when will the account have a sufficient amount to fund four years of college?
  1. A $3200 investment is invested at 3.25% annual interest compounded monthly.
  2. Determine the amount of interest earned after four years.
  3. How much will be in the account after 8 years?
  1. When will the account contain $250,000?
  1. A $150,000 investment is invested at 2.2% annual interest compounded quarterly.
  2. How much interest is earned after 12 years?
  3. How long will it be before the account triples?
  4. How much interest is earned at this time?
  1. The Fresh and Green Company has a savings plan for employees. If an employee makes an initial deposit of $5000, the company pays 3% interest compounded bimonthly (every 2 months).
  1. If an employee withdraws the money after five years, how much is withdrawn?
  2. When will the account contain $16143.18?
  3. When will the account double?
  4. Find the interest earned if the money is withdrawn after 35 years.
  1. Mr. and Mrs. Boyce bought a house for $205,000 in 1995. Real estate values in their area decreased approximately 2% each year until the year 2012.
  2. What was the value of the house in 2012?
  1. If the market increases at a rate of 3% from 2012 on, when will be the value of the house be worth $205,000 again?
  1. The Greens bought a condo for $185,000 in 2005.
  2. If its value appreciates at 4% per year, what will the value be in 2015?
  3. What year will the condo be worth $352,784.90?
  4. An isotope of cesium (cesium-137) has a half-life of 30 years. If 3.0 g of cesium-137 disintegrates over a period of 60 years.
  5. How many g of cesium-137 would remain?
  6. When will the amount be 0.0097669g?
  1. Actinium-226 has a half-life of 29 hours. If 250 mg of actinium-226 disintegrates over a period of 153 hours.
  2. How many mg of actinium-226 will remain?
  3. When will the amount be about 0.93mg?
  1. The half-life of radon-222 is 3.8 days.
  2. How much of a 60 g sample is left after 15.2 days?
  3. When will the amount be equal to 1g?
  4. Will the radon-222 ever be completely gone? Explain your answer.
  1. In 1985, there were 495 cell phone subscribers in the small town of Centerville. The number of subscribers increased by 75% per year after 1985.
  1. How many cell phone subscribers were in Centerville in 1998?
  2. How long before there are one million users?
  3. How long before there will be two million users?
  1. Bacteria can multiply at an alarming rate when each bacteria splits into two new cells, thus doubling. If we start with only one bacteria which can double every hour.
  2. How many bacteria will we have by the end of three day?
  3. How many hours will it take for the bacteria to reach one million?
  1. Each year the local country club sponsors a tennis tournament. Play starts with 256 participants. During each round, half of the players are eliminated.
  2. How many players remain after 6 rounds?
  3. How many rounds are required to leave 32 players in the tournament?
  1. You have inherited land that was purchased for $20,000 in 1960. The value of the land increased by approximately 205% per year.
  2. What is the approximate value of the land in the year 2015?
  3. When will the land be worth $11,649,000.00?
  1. An adult takes 600 mg of ibuprofen. Each hour, the amount of ibuprofen in the person’s system decreases by about 29%.
  2. How much ibuprofen is left after 5 hours?
  3. It is safe to take ibuprofen again once there is only 30 mgs of ibuprofen left in a person’s system. Eight hours after taking 600 mg of ibuprofen, would it be safe to take more ibuprofen?
  4. Gina deposited $2500 in an account that pays 1.5% interest compounded continuously.
  5. What will the balance be in 10 years?
  6. How long will it take the account to double?
  7. The Browns have a savings account to help pay for their daughters tuition to Harvard. The bank pays 1.5% interest on the savings account, compounded continuously. Their initial investment is $1700.00 was deposited when their child was born in 2007. Tuition is $58607.00 this year (2014-2015) and increases by .05% each year. They plan for their daughter to attend the year 2025.
  8. Find the total balance after three years.
  9. Will there be adequate funds in the account for her first year of school?
  1. A $2500 investment is invested at 5.25% annual interest compounded continuously.
  2. How much is in the account after 4 years?
  3. How much interest is earned after 6 years?
  4. How long will it take the account to double?
  5. How long will it take the account to triple?
  1. A $100,000 investment is invested at 5.2% annual interest with continuous compounding.
  2. How much will be in account after 5 years?
  3. How much interest is earned after 10 years?
  4. When will the account reach 1 million dollars?
  1. The Fresh and Green Company has a savings plan for employees. If an employee makes an initial deposit of $1000, the company pays 8% interest compounded continuously.
  2. If an employee withdraws the money after five years, how much is withdrawn?
  3. If the employee wishes to have $20,000.00 for a down payment on a house. How long will he need to leave the money in the account?
  4. How much interest will be earned after 25 years?

23. The Parker family plan to save a set amount P each year for each of their children’s college funds. They used the formula , where A is the amount college tuition will cost in n years, and i is the yearly interest, to find the amount they must save for each child. In 18 years, the Parkers expect college tuition to cost $48,000.

a. How much must they save each year, per child, at an interest rate of 7.5%?

b. How much must they save per child if the interest rate is 8.25%?

24. The future value Fn of an annuity type of investment is given by the expression , where P is the periodic payment, n is the number of payments, and i is the interest rate over the period of each payment. Samantha plans to save $2200 each year for 45 years, at an annual interest rate of 6.25%.

a. How much will she have in her account at the end of that time?

b. How much will she have if she saves for 40 years at an interest rate of 8.5%?

25. A shipping company owns a fleet of heavy trucks. If the purchase price of each truck is $245,000 and its value depreciates by 15 percent per year, what is the value of each truck after 4 years?

26.Mexico City, Mexico, is the world’s second largest metropolis and is also one of its fastest-growing cities with a projected growth rate of 3.2% per year. Its population in 1991 was 20,899,000 people. Use the formula to predict its population P in millions with t equal to the number of years after 1991. What is the predicted population to the nearest thousands of Mexico City for the year 2010?

27. A sporting goods company has observed a decline in sales following the end of each of its advertising campaigns. The decline in sales follows the formula , where S is the monthly sales in millions of dollars and t is the number of months after the end of the advertising campaign.
a. What will the monthly sales be three months after the end of the current campaign, rounded to the nearest hundred thousand dollars?

  1. How long after the campaign has ended will sales reach 1.37 million?

28. Among various populations of plants or animals, diseases spread exponentially. Use the function to model the spread of potentially lethal Newcastle disease among a flock of 325 turkeys on a turkey farm, with t equal to the number of days since the first case of the disease.

a. How many birds will be infected with Newcastle disease after 7 days?

b. If not treated when will be turkey population on the farm be depleted?

29. The Ebbinghaus model of human memory may be used to model the amount of acquired knowledge a college student will retain after “cramming” for a final exam. The formula is , where a and b vary from one person to another, and p is the percent of retained knowledge day later when the student actually takes the final exam. If a = 20 and b = 1.2 for a typical student, how much of their “crammed” knowledge will that student retain at the moment of taking the final exam?

math III

Answer Section

SHORT ANSWER

1.ANS:

a. $1345.39 per child

b. $1250.85 per child

OBJ:11-2.3 Solve problems involving exponential growth and decay.

STO:GA 30, GA 31, GA 4TOP:Solve problems involving exponential growth and decay.

KEY:Solve Problems, Exponential Growth, Exponential Decay

2.ANS:

a. $503,497.43

b. $650,501.58

OBJ:11-2.3 Solve problems involving exponential growth and decay.

STO:GA 30, GA 31, GA 4TOP:Solve problems involving exponential growth and decay.

KEY:Solve Problems, Exponential Growth, Exponential Decay

3.ANS:

$127,891.53

OBJ:11-2.3 Solve problems involving exponential growth and decay.

STO:GA 30, GA 31, GA 4TOP:Solve problems involving exponential growth and decay.

KEY:Solve Problems, Exponential Growth, Exponential Decay

4.ANS:

38,386,000

OBJ:11-3.1 Use the exponential decay function y = e^x.STO:GA 30, GA 31, GA 4

TOP:Use the exponential decay function y = e^x.KEY:Exponential Decay

5.ANS:

$26,000,000

OBJ:11-3.1 Use the exponential decay function y = e^x.STO:GA 30, GA 31, GA 4

TOP:Use the exponential decay function y = e^x.KEY:Exponential Decay

6.ANS:

211

OBJ:11-3.1 Use the exponential decay function y = e^x.STO:GA 30, GA 31, GA 4

TOP:Use the exponential decay function y = e^x.KEY:Exponential Decay

7.ANS:

93.6%

OBJ:11-3.1 Use the exponential decay function y = e^x.STO:GA 30, GA 31, GA 4

TOP:Use the exponential decay function y = e^x.KEY:Exponential Decay