Billy B.

# solve problem

A toy tractor sold for $231 in 1975 and was sold again in 1987 for$455. Assume that the growth in the value V of the collectors item was exponential.

Find the value K of the exponential growth rate. Assume V=\$231

## 2 Answers By Expert Tutors

By:

Tutor
New to Wyzant

Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors

Stephanie M.

tutor
For posterity:

I've been looking through my old answers and, although this one is several months old, I feel I ought to explain a bit about exponential growth just in case another student happens upon it.

First, it's important to note that there's no specific "exponential growth rate formula." Exponential growth describes any situation in which something is increasing exponentially. That is, exponential growth occurs whenever you see the variable in the exponent. So, a basic exponential growth formula looks like this: P(t) = a(r)t. Replacing r with the constant e gives you one exponential growth formula, usually used for computing continuously-compounded interest. It's not really applicable in this particular case.

Second, in any exponential growth formula, you can immediately pick out the rate of growth r and the initial amount a. So, P(t) = 50(1.2)t models a situation where we started with 50 of something and it grew at a rate of 1.2, or 120%. That is, it increased 20% each year. You can tell when a quantity is increasing because the rate will be over 1. Anything under 1 indicates an exponential decrease.

Since the rate always appears in a specific place in the formula (in the base, not in the exponent), you should not solve for a variable in the exponent and call it the rate, as Andrew does. And, if the rate of growth for something you know is increasing comes out to be less than one (as in Andrew's answer, where k=0.0565), you ought to check your work---this is a good indication that you've done something wrong.

Therefore, please use the second answer (below) as a guide for problems like this, not the first.
Report

04/23/16

Andrew M.

Stephanie,
We are told to assume the growth rate is exponential.
Thus, we have to use the exponential growth rate formula  P(t) = Poekt

For this problem our original equation to solve becomes 455 = 231e12k
From this we solve for k
Report

06/19/15

Andrew M.

Stephanie,
This problem states we assume the growth is exponential; thus we have to use the exponential growth rate formula
P(t) = Poekt

For this problem we have 455 = 231e12k and we must solve for k
Report

06/19/15

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