Exponential Growth and Decay

Multiplier for a Percent Increase Change the percent increase to a decimal and add the result to 1. Example: What is the multiplier for a 5% increase? First Step: Second Step: . . . 5.% = 0.05 2 1 Multiplier

Multiplier for a Percent Decrease Change the percent decrease to a decimal and subtract the result from 1. Example: What is the multiplier for a 17% decrease? First Step: Second Step: . . 17.% = . 0.17 2 1 Multiplier

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)

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)

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

V(x) = 10,000 ( 1.08 )x Growth and Decay Chet 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 2,000,000. 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

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 ( 1.035 )x