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Exponential growth word problem

First-class postage (for the first ounce) was $.20 in 1981 and $.37 in 2002. Assume the cost increases according to an exponential growth function.

A) Let t=0 correspond to 1981 and t=21 correspond to 2002. Then t is the number of years since 1981. Use the data points (0,20) and (21,37) to find the exponential growth rate and fit an exponential growth function P(t)=Poe^kt to the data, where P(t) is the cost of first-class postage, in cents, t years after 1981.

B) Use the function found in part (a) to predict the cost of first-class postage in 2008.

C) When will the cost of first-class postage be $1.00 or one hundred cents?

Solution Preview

A) Suppose P(t) = Po * e^(kt)
When t = 0, we have P(0) = Po = 0.20
When t = 21, we have P(21) = Po * e^(21k) = 0.20 ...

Solution Summary

This provides an example of working with an exponential growth function with postage.