8 1 Exponential Growth 8 2 Exponential Decay

8. 1 Exponential Growth 8. 2 Exponential Decay

Exponential Function An exponential function has a positive base other than 1. The general exponential function is

The graph of y = x b Graph. Exponent ial function. tii Asymptote – a line that a graph approaches as you move away from the origin. ( The graph never touches the line. ) If b is greater than 1 the graph is an exponential growth. b>1 If b is greater than 0 but less than 1 the graph is an exponential decay. 0<b<1 ( A reflection in the y direction. )

The graph of y = x-h ab +k Graph. Exponential function. tii If a is negative the graph will reflect in the x direction. The absolute value of a changes the y- intercept. The h shifts the graph horizontally. (left or right) The k shifts the graph vertically. (up or down)

Exponential Growth Model Instead of x, t is the variable. (1+r) is called the growth factor. a is the initial amount. y is the amount after t years.

Exponential Growth Compound Interest A is the balance. P is the principal deposited in an account. r is the interest rate changed to a decimal (% 100). n is the number of times the interest is compounded in a year. Annually n=1 Semiannually n=2 Quarterly n=4 Monthly n = 12

Compound Interest Problem You deposit $500 in an account that pays 3% interest. Find the balance after 2 years if the interest is compounded quarterly. A=? P = $500

Exponential Decay Model y is the quantity after t years. t is the variable. a is the initial amount. (1 -r) is the decay factor.

Exponential Decay Depreciation You buy a new car for $22, 000. The value of the car decreases by 12. 5%. What is the value of the car after 4 years. y=? a = $22, 000