Exponential Growth and Decay Exponential Growth AP1r A

Exponential Growth and Decay

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

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

Growth and Decay The area of a rain forest is 20, 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 (. 89 ) 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

Growth and Decay The population of people in Upper Darby is 2, 000. Every year the population will decrease by 19%. Write an equation y that will predict the population after x years. y = 2, 000 (. 81 ) 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 ( 1. 035 ) x

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

You try: • 2) Collin’s business had a profit of $25, 000 in 1998. 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?

• Sophia invests $1000 in a company. After 5 years your investment is worth $2125. 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?

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 25 mg of iodine-131, how much would be left after 32 days or 4 half-lives.

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.

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?

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?