Section 8

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Section 8 8 Exponential Growth Decay

• Objectives
• To model exponential growth
• To model exponential decay

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Population Growth in Florida

• In 1990, Floridas population was about 13
  million. Since 1990, the states population has
  grown about 1.7 each year. This means Floridas
  population is growing exponentially.

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To find Floridas population in 1991, multiply
the 1990 population by 1.7 and add this to the
1990 population.
 
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Exponential Growth

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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.

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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.
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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.

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

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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.

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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.

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• 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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Textbook Page 441 1 19 All
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Section 8 8 Continued

• Objectives
• To model exponential decay

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Exponential Decay

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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?

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• 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.
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• 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 1990.
b. Use your equation to find the population of
Washington, D.C., in 2010.
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Example 5 Exponential Growth or Decay

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Homework

• 8 8 Practice Ditto