8.2 Exponential Decay

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8.2 Exponential Decay
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• Exponential decay function- just like growth but
  is in the form where a gt 0 and 0 lt b lt 1

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Graph exponential decay functions using y abx -
h k

• 1. Graph
• 2. Graph
• 3. Graph

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• When a real-life quantity decreases by a fixed
  percent each year (or other time period), the
  amount y of the quantity after t years can be
  modeled by this equation y a(1 r)t
• In this model, a is the initial amount and r is
  the percent decrease expressed as a decimal. The
  quantity 1 r is called the decay factor.

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• 1. You drink a beverage with 120 milligrams of
  caffeine. Each hour, h, the amount c of caffeine
  in your system decreases by about 12.
• Write an exponential decay model.
• How much caffeine remains in your system after 3
  hours?
• 2. You buy a new computer for 2100. The value
  of the computer decreases by about 50 annually.
  
• Write an exponential decay model for the value of
  the computer. Use the model to estimate the
  value after 2 years.
• Graph the model
• Estimate when the computer will be work 600.

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• 3. In Oswego there are 40,000 homes on septic
  systems. Each year 10 of the homes are expected
  to disconnect from septic systems and connect to
  the sewer systems.
• How many homes will still be on septic in 5
  years?
• When will there be about only 17,200 homes not
  on a sewer system?
• 4. A new car costs 23,000. The value decreases
  by 15 each year. Write a model to estimate the
  value after 3 years and predict the time the car
  will be worth half its value.