Exponential Functions, Half-Life and Compound Interest

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

• y = 5000(0.7)^x

• y = 30(5000)^x

• y = 5000(1.3)^x

• y = 5000(0.3)^x

A population of fish starts at 8,000 and decreases by 6% per year. What is the approximate population of fish after 10 years?

• 14327

• 4309

• 839

• 7680

The half-life of strontium-90 is 25 years. How much strontium-90 will remain after 100 years if the initial amount is 4.0 g?

• 3.0g

• 0.25mg

• 0.3g

• 0.25g

A population growing at an annual rate r will triple in a time t given by the formula A = (1 + r)^t. If the growth rate remains constant and equals 6% per year, about how long will it take the population of the town to triple?

• 18.3 years

• 8 years

• 0.8 years

• 1.8 years

Caiden earned $475 from mowing lawns last summer. He deposited this money in an account that pays an interest rate of 3.8% compounded annually. What will be his balance after 15 years?

• $827.52

• $831.10

• $839.45

• $846.80

What amount would need to be invested at 4% interest compounded quarterly in order to have $4500 in 5 years?

• $5490.86

• $3366.58

• $3687.95

• $3903.18

Kennedy won $3,000 from a radio contest. If she puts this money in a bank account that earns 2.9% interest compounded quarterly, how much will she have in her account in 10 years?

• $4915.59

• $3933.28

• $2979.81

• $4005.09

Given an investment of $1,500:

Which investment would have a larger balance after 5 years?

• Option 1: 4% compounded monthly

• Option 2: 3.9% compounded daily

The population of Eden is growing continuously at a rate of 1.9%. If the current population is 15,230, about how many years will it take for the population to reach 20,000?

• 31

• 2

• 15

• 68

Marcus is buying a new Jet Ski for $12,500. He is considering 2 credit options. Option A offers a 6 year loan with 8.5% interest compounded quarterly, while Option B offers a 5 year loan with 10% interest compounded annually. Which option is better and how much will he save?

• $495.21 saved

• $573.83 saved

• $495.21 saved

• $573.83 saved