Applications of Exponential Functions

1
Applications of Exponential Functions
2
Population Growth

• Population growth can be modeled by the basic
  form of the exponential function y abx.
• Growth b gt 1
• b growth factor
• a initial amount
• x time
• y ending amount

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Population Growth

• In 2003, the population of the popular town of
  Smithville was estimated to be 35,000 people with
  an annual rate of increase (growth) of about
  2.4.
• What is the growth factor?
• After one year 35,000 (0.024)(35,000)
• Factor out 35,000
• 35,000(1 0.024) 35,000(1.024)
• So, the growth factor is 1.024

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Population Growth

• 2. Write an equation to model future population
  growth in Smithville.
• y abx
• y a(1.024)x
• So, y 35,000(1.024)x, where x is the number of
  years since 2003.

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Population Growth

• 3. Use the equation that youve written to
  estimate the population of Smithville in 2007 to
  the nearest one hundred people.
• y 35,000(1.024)4 38,482.91 38,500

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Compound Interest

• What is interest?
• Compound Interest Interest that is earned on
  both the principal and any interest that has been
  earned previously.
• Balance The sum of the Principal and the
  Interest

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Compound Interest

• Formula
• A the ending amount
• P the beginning amount (or "principal)
• r the interest rate (expressed as a decimal)
• n the number of compoundings in a year
• t the total number of years

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Compound Interest

• Jackie deposits 325 in an account that pays 4.1
  interest compounded annually. How much money will
  Jackie have in her account after 3 years?
• A 325(1 0.041)1(3)
• 1
• A 325(1.041)3
• A 366.64
• Jackie will have 366.64 in her account after 3
  years.