1. Exponential Decay –Modeled with the function: y = a b x for a > 0 and 0 < b < 1. y = a b x a = the starting amount (when x = 0) b = the base, which is between 0 and 1, is the decay factor x = exponent 8.8 Exponential Growth and Decay Cont.

2. Modeling Exponential Decay Since 1980, the number of gallons of whole milk each person in the United States drinks each year has decreased 4.1% each year. In 1980, each person drank an average of 16.5 gallons of whole milk per year. a. Write an equation to model the gallons of whole milk per year. Relate: y = a b x Define: Let x = the number of years since 1980 Let y = the consumption of whole milk, in gallons Let a = 16.5, the initial number of gallons in 1980 Let b = the decay factor, which is 100% - 4.1% = 95.9% = 0.959 Write: y = 16.5 0.959 x

3. Modeling Exponential Decay b. Use your equation to find the approximate cost per day in 2000. y = 16.5 0.959 x y = 16.5 0.959 20 y ≈ 7.1 The average annual consumption of whole milk in 2000 was about 7 gal/person.

4. More Practice!!!! Homework - Textbook – p. 441 – 442 #2 – 30 even.