6.1 Exponential Growth and Decay Date: ______________

Warm-Up Rewrite each percent as a decimal. 1.) 8%2.) 2.4%3.) 0.01% Evaluate each expression for x = 3. 4.) 2x2x 5.) 50(3) x 6.) 2 2x

Exponential Functions An equation of the form y = ab x Examples y = 2(5) x y = 0.9(4.2) x If b > 1, then the function models exponential growth. If 0 < b <1, then the function models exponential decay.

Classify each as exponential growth or exponential decay. 1) 2) 3) 4) 5) 6) Exponential Growth Exponential Growth Exponential Growth Exponential Decay Exponential Decay Exponential Growth

A population of 10 hamsters will triple every year for 4 years. What will be the population after 4 years? y = ab t b = growth factor a = start value t = # of time periods

A population of 1000 bacteria will double every hour. What will be the population after 24 hours? after 5 days? y = ab t b = growth factor a = start value t = # of time periods

Exponential Functions Involving Percent of Increase A colony of 10,000 ants can increase by 15% in a month. How many ants will be in the colony after 1 year? y = a(1 + r) t r = % increase a = start value t = # of time periods

A baby weighing 7 pounds at birth may increase in weight by 11% per month for the first 12 months. How much will the baby weigh after 1 year?

A deposit of $1500 in an account pays interest compounded annually. How much will be in the account after 8 years?

A radioactive material decays at 10% per year. How much of the 12 pound material will be left after 20 years? y = a(1 − r) t r = % decrease a = start value t = # of time periods Exponential Functions Involving Percent of Decrease

Find the value of a downtown office building that cost 12 million dollars to build 20 years ago and depreciated at 9% per year.