Section 8 – 8 Exponential Growth & Decay Objectives: To model exponential growth To model exponential decay

Population Growth in Florida In 1990, Florida’s population was about 13 million. Since 1990, the state’s population has grown about 1.7% each year. This means Florida’s population is growing exponentially.

To find Florida’s population in 1991, multiply the 1990 population by 1.7% and add this to the 1990 population.

Exponential Growth

Example 1 Modeling Exponential Growth A)Since 1985, the daily cost of patient care in community hospitals in the United States has increased about 8.1% per year. In 1985, such hospital costs were an average of $460 per day.

Example 1 Modeling Exponential Growth B)Suppose your school has 4512 students this year. The student population is growing 2.5% each year. a. Write an equation to model the student population. b. Use your equation to determine the student population in 3 years.

Example 2 Compound Interest A)Suppose your family deposited $1500 in an account paying 6.5% interest compounded annually (once a year) when you were born. Find the account balance after 18 years.

B)Suppose you deposit $1000 in a college fund that pays 7.2% interest compounded annually. Find the account balance after 5 years.

Compound Interest 1)If interest is compounded more than once a year, you need to divide the interest rate by the number of interest periods. 2)To find the number of payment periods, you multiply the number of years by the number of interest periods per year.

Example 3 Compound Interest A)Suppose you deposited $1500 in an account paying 6.5% interest compounded quarterly. Find the account balance after 18 years.

B)Suppose you deposit $200 into an account earning 5%, compounded monthly. How much will be in the account after 1 year? 2 years? 5 years?

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Section 8 – 8 Continued… Objectives: To model exponential decay

Exponential Decay

Example 4 Exponential Decay A)Suppose the value of a $1200 computer decreases 27% annually. What will be the value of the computer after 3 years?

B)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 drunk per person. b. Use your equation to find the approximate consumption per person of whole milk in 2000.

C)Since 1990, the population of Washington, D.C., was about 604,000 people. Since then the population has decreased by about 1.8% per year. a. Write an equation to model the population of Washington, D.C., since b. Use your equation to find the population of Washington, D.C., in 2010.

Example 5 Exponential Growth or Decay

Homework 8 – 8 Practice Ditto;