Before we begin let’s do an activity!!! Paper folding Tonight’s Homework: Exponential Growth/Decay Worksheet Take out a pieces of and fold it in half. Fold it in half again, record the results, then fold again, and record the results. How many regions would result if the paper was folded 25 times?

Folds and Regions Recording Sheet

Connections YES!! This is an example of an exponential Is there a relationship between the number of folds and the number of regions? YES!! This is an example of an exponential function. The input “x” is an exponent

Pg 325

Exponential Growth

f (x) = 3 · 5x y = 250 · 1.065x g(t) = 3.5t h(x) = 5 · 1.02x Identify the initial amount “a” and the growth factor “b” in each exponential function. f (x) = 3 · 5x y = 250 · 1.065x g(t) = 3.5t h(x) = 5 · 1.02x

Exponential Growth Identify the original amount and the growth factor in the exponential function

Growth Factor

Exponential Growth 100% represents the original number, and you need to make that number “grow” by ___%. What is 100% as a decimal? For example, how could we show 14% growth?

Example 1 A town has 8496 people. The population is increasing at a rate of 3.5% per year. How many people will there be in 5 years? a = b = x =

Example 2 A population of rabbits doubles every six months. Assume that you begin with 8 rabbits. How many rabbits will there be after 4 years? a = b = x =