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Exponential Growth/Decay
Exponential Growth Formula
N(t) = Noekt k > 0
~ k is known as the constant of proportionality.
~ k a rate - the rate of growth or decay.
~ If k > 0, then we are finding exponential growth.
~ If k < 0, then we are finding exponential decay.
~ No - the initial amount.
~ t - time
~ N(t) - the answer
Example 3
A pizza is removed from the oven at a temperature of 425° F.
After 15 minutes, the pizza has cooled to 200° F.
Use an exponential decay model to find the approximate decay rate.
N(t) = Noekt k > 0
200 = 425 e15r
Work and solution
If the exponential equation has e as its base, we can solve an equation of this type using the following property:
ln ex = x i.e. ln e2x + 5 = 2x + 5
200 = 425e15r
200/425 = e15r The variable, r, is the unknown.
ln 200/425 = ln e15r Use the property: ln ex = x
-.7538 = 15r
-.7538/15 = r
-.0503 = r The rate is negative, indicating that it is an exponential decay.
5% decay
Exponential Growth Problem
The following problem is an example of how to solve exponential growth word problems.
Read the problem and the questions first.
Do the problems before you look over the answers.
Exponential_Growth_2.pdfGoogle Sites
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