Solve the problem.
-Suppose that the amount of oil pumped from a well decreases at the continuous rate of 12% per year. When, to the nearest year, will the well's output fall to one-eighth of its present value?
A) 17 years
B) 12 years
C) 26 years
D) 2 years

Question

Quizplus · Accepted Answer

The problem involves exponential decay. The formula for exponential decay is $ A = P e^{-rt} $, where $ A $ is the final amount, $ P $ is the initial amount, $ r $ is the rate of decay, and $ t $ is time. We need to find $ t $ when $ A = \frac{1}{8}P $ and $ r = 0.12 $. Solving $ \frac{1}{8}P = P e^{-0.12t} $ gives $ t \approx 17 $ years.

Solve the Problem. -Suppose That the Amount of Oil Pumped from a Well