Suppose that the amount of oil pumped from a well decreases at the continuous rate of 9% per year. When, to the nearest year, will the well's output fall to one-eighth of its present value?
A) 23 years
B) 35 years
C) 2 years
D) 15 years

Question

Quizplus · Accepted Answer

The problem can be solved using the formula for exponential decay, $A = P(1 - r)^t$, where $A$ is the amount after time $t$, $P$ is the initial amount, $r$ is the rate of decay (as a decimal), and $t$ is the time in years. We want $A$ to be $\frac{1}{8}$ of $P$, and $r$ is 0.09 (9%). Rearranging the formula to solve for $t$, we get $t = \frac{\ln(A/P)}{\ln(1 - r)}$. Substituting $A/P = \frac{1}{8}$ and $r = 0.09$, we find $t$ is approximately 23 years.

Suppose That the Amount of Oil Pumped from a Well