7 7 Exponential Growth and Decay Exponential Growth

7 -7 Exponential Growth and Decay

Exponential Growth x the amount of time a represents the initial amount

Problem 1: Modeling Exponential Growth Since 2005, the amount of money spent at restaurants in the US has increased about 7% each year. In 2005, about $360 billion was spent at restaurants. If the trend continues, about how much will be spent at restaurants is 2015?

Identify the initial amount a and the growth factor b in each exponential function. (Hint: In the exponential equation y = a • bx, a is the initial amount and b is the growth factor when b > 1. ) 1. f (x) = 2 • 3 x 3. y = 6 x 2. y=5

Compound Interest • When a bank pays interest on both the principal and the interest an account already earned, the bank is paying compound interest • Compound Interest is an example of exponential growth

Compound Interest Formula

Problem 2: Compound Interest Suppose that when you friend was born, your friend’s parents deposited $2000 in an account paying 4. 5% interest compounded quarterly. What will the balance in the account be after 18 years?

Find the balance in each account after the given period. $5000 principal earning 4% compounded annually, after 10 years

Exponential Decay x the amount of time a represents the initial amount

Problem 3: Modeling Exponential Decay

Identify the initial amount a and the decay factor b in each exponential function. (Hint: In the exponential equation y = a • bx, a is the initial amount and b is the decay factor when b < 1. ) 1. y = 4 • 0. 2 x 2. f (x) = 3 • 0. 9 x

Tell whether the equation represents exponential growth, exponential decay, or neither. 1. y = 2 • 3 x 2. f (x) = 6 • 0. 5 x 3. f (x) = 5 • x 2 4. y = 0. 3 x