Choose the one alternative that best completes the statement or answers the question.
-Suppose the consumption of electricity grows at $6.3 \%$ per year, compounded continuously. Find the number of years before the use of electricity has tripled. Round the answer to the nearest hundredth.
A) $17.44 \mathrm { yr }$
B) $0.17 \mathrm { yr }$
C) $47.62 \mathrm { yr }$
D) $1.74 \mathrm { yr }$

Question

Quizplus · Accepted Answer

To find the number of years before the use of electricity has tripled when growing at a rate of 6.3% per year compounded continuously, we use the formula for continuous compounding: $A = Pe^{rt}$, where $A$ is the amount after time $t$, $P$ is the initial amount, $r$ is the rate of growth, and $e$ is the base of the natural logarithm. Since we want the amount to triple, $A/P = 3$. Rearranging the formula and solving for $t$, we get $t = \frac{\ln(A/P)}{r} = \frac{\ln(3)}{0.063}$, which calculates to approximately 17.44 years.

Choose the One Alternative That Best Completes the Statement or Answers