1. 8-8: E XPONENTIAL G ROWTH AND D ECAY Essential Question: Explain the difference between exponential growth and decay

2. 8-8: E XPONENTIAL G ROWTH /D ECAY Exponential growth y = a ● b x Note that this is the same as any old exponential function, except that the base in exponential growth is always greater than 1. Why? Starting amount (when x = 0) Base (greater than 1) Exponent

3. 8-8: E XPONENTIAL G ROWTH /D ECAY Example 1: Modeling Exponential Growth Since 1995, the daily cost of patient care in hospitals in the United States has increased about 4% per year. In 1995, such hospital costs were an average of $968 per day. Part A: Write an equation to model the cost of hospital care since 1995. y = a ● b x Let x = the number of years since 1995 Let y = the cost of hospital care Let a = the initial cost in 1995, $968 Let b = the growth factor 100% + 4% = 104% = 1.04 y = 968 ● 1.04 x

4. 8-8: E XPONENTIAL G ROWTH /D ECAY Part B: Use your equation to estimate the approximate cost per day in 2015 y = 968 ● 1.04 x Since our function starts in 1995, 2015 is 20 years later y = 968 ● 1.04 20 y = $2121.01 The cost per day in 2015 will be about $2121.

5. 8-8: E XPONENTIAL G ROWTH /D ECAY Your Turn Suppose your school district has 4512 students this year. The student population is growing 2.5% each year. A) Write an equation to model the student population y = 4512 ● 1.025 x B) What will the student population be in 3 years? About 4859 students

6. When a bank pays interest on both the principal and the interest an account has already earned, the bank is paying compound interest. An interest period is the length of time over which interest is calculated. Example 2: Compound Interest Suppose your parents deposited $1500 in an account paying 3.5% interest compounded annually (once a year) when you were born. Find the account balance after 18 years. y = a ● b x y = 1500 ● 1.035 18 y = $2786.23

7. 8-8: E XPONENTIAL G ROWTH /D ECAY Your Turn Suppose your parents invested $1500 at 4% interest compounded annually instead. How much would the account be after 18 years? $3038.72

8. Exponential decay y = a ● b x Note that this is the same as exponential growth, except the base is between 0 and 1. Why? Starting amount (when x = 0) Base (between 0 and 1) Exponent

9. 8-8: E XPONENTIAL G ROWTH /D ECAY Example 3: Modeling Exponential Decay Since 1980, the number of gallons of whole milk each person in the US drinks each year has decreased 4.1%. In 1980, each person drank an average of 16.5 gallons of whole milk per year. Part A: Write an equation to model the amount of milk consumed since 1980. y = a ● b x Let x = the number of years since 1980 Let y = the number of gallons drunk Let a = the initial amount in 1980, 16.5 Let b = the decay factor 100% - 4.1% = 95.9% = 0.959 y = 16.5 ● 0.959 x

10. 8-8: E XPONENTIAL G ROWTH /D ECAY Part B: Use your equation to estimate the approximate consumption of milk in 2020 y = 16.5 ● 0.959 x Since our function starts in 1980, 2020 is 40 years later y = 16.5 ● 0.959 40 y = 3.1 The average consumption in 2020 will be about 3.1 gal/person

11. 8-8: E XPONENTIAL G ROWTH /D ECAY Your Turn In 1990, the population of Washington, DC was about 604,000 people. Since then, the population has decreased about 1.8% per year. A) Write an equation to model the student population y = 640,000 ● 0.982 x B) What was the population in 2010? About 420,017 people

12. Assignment Worksheet #8-8 Problems 1 – 9, odds