1. Exponential Growth and Decay and Compound Interest
Unit 9
Exponential Growth and Decay and Compound Interest

2. Exponential growth- occurs when a quantity increases by the same rate r in each period t. When this happens, the value of the quantity at any given time can be as a function of the rate and the original amount.
A = Pert

3. The original value of a painting is $9000 and the value increases by 7% each year. Write an exponential growth function to model this situation. Then find the painting’s value in 15 years.
You bought a sculpture for $1200. You know that it appreciates at a rate of 8% per year. You want to sell it when it triples in value. When should you sell it?

5. Write a compound interest function to model each situation
Write a compound interest function to model each situation. Then find the balance after the given number of years. $1200 invested at a rate of 2% compounded quarterly for 3 years.

6. Write a compound interest function to model each situation
Write a compound interest function to model each situation. Then find the balance after the given number of years. $15000 invested at a rate of 4.8% compounded monthly for 2 years.

7. If I won $1 million dollars, could I live off the interest ($50000 per year) if I got 1.05% rate compounded monthly?

8. I want to save for my daughter’s college
I want to save for my daughter’s college. I want to have $250,000 when she graduates high school (13 years). I am going to invest it where the return is a rate of 5% compounded monthly and not put anymore in. How much do I need to initially invest to have that I have enough in 13 years?

9. Compounded continuously

10. Suppose $5000 is put into an account that pays 4% compounded continuously. How much will be in the account after 3 years?

11. If I deposited $20,000 into an account with a rate of 0.5% for 5 years. How much would I have if it was compounded weekly, monthly, quarterly, yearly, and continuously.

12. Would it be better for me to deposit my $1 million dollars into my 1% compounded monthly account or an account compounded continuously at 0.9%?

13. Exponential Decay- occurs when a quantity decreases by the same rate in each time period t. Just like exponential growth, the value of the quantity at any given time can be calculated by using the rate and the original amount.

14. The population of a town is decreasing at a rate of 3% per year
The population of a town is decreasing at a rate of 3% per year. In 2000 there were 1700 people. Write and exponential decay function to model this situation. Then find the population in 2012.

15. The fish population in a local stream is decreasing at a rate of 3% per year. The original population was Write an exponential decay function to model this situation. Then find the population after 7 years.

16. Half- Life (cuts in half each half life)
Astatine-218 has a half life of 2 seconds. Find the amount left from a 500 gram sample of astatine-218 after 10 seconds.