1. Exponential Growth and Decay

2. A = P ( 1 + r ) t Exponential Growth A: Amount after time t
P: Principle (starting amount)
t: Time after starting point
r: Decimal increase (% ÷ 100)

3. A(t) = P ( 1 – r ) t Exponential Decay
A(t): Amount as a function in terms of t
P: Principle (starting amount)
t: Time after starting point
r: Decimal decrease (% ÷ 100)

4. Growth and Decay
The area of a rain forest is 20,000,000 square miles. Every year, 11% of the rain forest will be destroyed. Write an equation that will find the remaining area y of the rain forest after x years.
y = 20,000,000 ( .89 )x

5. V(x) = 10,000 ( 1.08 )x Growth and Decay
Bailey is going to put $10,000 into a bank account. Every year the value of the account will increase by 8%. Write a function V that will determine the value of the account after x years.
V(x) = 10,000 ( 1.08 )x

6. Growth and Decay
The population of people in Upper Darby is 2,000,000. Every year the population will decrease by 19%. Write an equation y that will predict the population after x years.
y = 2,000,000 ( .81 )x

7. V(x) = 165,000 ( 1.035 )x Growth and Decay
The value of a home worth $165,000 will increase by 3.5% every year. Write a function V that will predict the value of a home after x years.
V(x) = 165,000 ( )x

8. A population of 20 rabbits is released into a wildlife region
A population of 20 rabbits is released into a wildlife region. The population triples each year.
How many bunnies
Are there in 5 years?
When will the
Bunny population
reach 1000?

9. You try:
2) Collin’s business had a profit of $25,000 in If the profit increased by 12% each year, what would his expected profit be in the year 2010?
3) How long did it take the profit to double?

10. Sophia invests $1000 in a company
Sophia invests $1000 in a company. After 5 years your investment is worth $ What is the rate of her return?
She invested $1000 in another company and 5 years later she only has $625. What is her rate of return for this company?

11. Iodine-131 is a radioactive isotope used in medicine
Iodine-131 is a radioactive isotope used in medicine. Its half-life or decay rate of 50% is 8 days. If a patient is given 25mg of iodine-131, how much would be left after 32 days or 4 half-lives.

12. Compound Interest Formula
P dollars invested at an annual rate r, compounded n times per year, has a value of F dollars after t years.
Think of P as the present value, and F as the future value of the deposit.

13. Examples
Josh’s credit card charges 12.2% interest compounded monthly. If he spents $220 this month, how much would his bill be at the end of 3 months?
Josh sees a credit card that offers 10.5% interest that is compounded quarterly. How much would he owe after 3 months with this card?

14. Compounded Continuously

15. A credit card company charges 22. 99% compounded continuously
A credit card company charges 22.99% compounded continuously. If you charged $500 this month how long would it take your bill to double?