6 1 Exponential Growth and Decay Date WarmUp

6. 1 Exponential Growth and Decay Date: _______

Warm-Up Rewrite each percent as a decimal. 1. ) 8% 2. ) 2. 4% 3. ) 0. 01% 0. 08 0. 024 0. 0001 Evaluate each expression for x = 3. 4. ) 2 x 5. ) 50(3)x 6. ) 22 x-1 8 1350 32

Exponential Functions An equation of the form y = a • bx 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) 4) Exponential Growth Decay 2) 5) Exponential Growth 3) Exponential Decay 6) Exponential Growth

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

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

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

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?

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

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