Solve the problem.
-Suppose the consumption of electricity grows at 5.8% per year, compounded continuously. Find the number of years before the use of electricity has tripled. Round the answer to the nearest hundredth.
A) 1.89 yr
B) 18.94 yr
C) 51.72 yr
D) 0.19 yr

Question

Quizplus · Accepted Answer

To find the number of years before the use of electricity has tripled when growing at a rate of 5.8% 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 values, we get $3 = e^{0.058t}$. Taking the natural logarithm of both sides gives $ln(3) = 0.058t$. Solving for $t$ gives $t = \frac{ln(3)}{0.058}$, which approximately equals 18.94 years.

Solve the Problem. -Suppose the Consumption of Electricity Grows at 5.8% Per Year