Write the word or phrase that best completes each statement or answers the question.
-Suppose the consumption of electricity grows at $4.5 \%$ per year, compounded continuously. Find the number of years before the use of electricity has tripled. Round the answer to the nearest hundredth.
A) $66.67 \mathrm { yr }$
B) $0.24 \mathrm { yr }$
C) $2.44 \mathrm { yr }$
D) $24.41 \mathrm { yr }$

Question

Quizplus · Accepted Answer

To find the number of years before the use of electricity has tripled when growing at a rate of 4.5% 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 electricity use to triple, $A/P = 3$. Substituting the given rate $r = 0.045$ and solving for $t$, we get $t = \frac{\ln(3)}{0.045}$, which approximately equals 24.41 years.

Write the Word or Phrase That Best Completes Each Statement 4.5%4.5 \%4.5%

Write the Word or Phrase That Best Completes Each Statement $4.5 \%$