4.5 Exponential Growth and Decay

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4.5 Exponential Growth and Decay
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Law of Exponential Growth and Decay

• If y is a positive quantity whose rate of change
  with respect to time is proportional to the
  quantity present at any time t, then

where C is the initial value and k is the
constant of proportionality. Exponential growth
is indicated by kgt0 and exponential decay by klt0.
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Radioactive decay is measured in terms of
half-life, the number of years required for half
of the atoms in a sample of radioactive material
to decay.
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Guidelines for Modeling Exponential Growth and
Decay
1. Use the given information to write two sets
of conditions



involving y and t. 2. Substitute
the given conditions into the model



and
use the results to solve for the constants C and
k.



(If one of the conditions involves t 0,
substitute that



value first to solve for C.) 3. Use
the model to answer the question.