Exponential Growth and Decay

M & M Lab Part 1- Growth What happened to the number of M&Ms? Part 2-Decay What happened to the number of M&Ms? Increased Decreased What was true about the values of a &b? a is the starting number of M&Ms b >1 a is the starting number of M&Ms b < 1

10.1– Exponential Funtions Ex. 1 Sketch the graph of y = 2 x. Then state the functions domain & range. *Sketch of graph must have y-intercept & four other coordinate points. Use the “table” function on your TI-83! xy

Ex. 2 Sketch the graph of y = (⅞) x. Then state the functions domain & range. xy

decay

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 = 1Semiannually 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