The consumption of electricity can be modeled by C $C = A e ^ { r t }$ , where A is the current use, r is the rate at which the use is increasing, and t is the number of years. Suppose the consumption of electricity grows at 6.8% per year.
Find the number of years before the use of electricity has tripled. Round the answer to the nearest hundredth.
A) 0.16 year
B) 44.12 years
C) 1.62 years
D) 16.16 years

Question

Quizplus · Accepted Answer

To find the number of years before the use of electricity has tripled, we set $C = 3A$ (since tripling the current use means the consumption becomes three times the initial amount). Substituting into the given formula, we get $3A = A e^{0.068t}$. Dividing both sides by $A$ and taking the natural logarithm of both sides gives $\ln(3) = 0.068t$. Solving for $t$ gives $t = \frac{\ln(3)}{0.068}$, which approximately equals 16.16 years.

The Consumption of Electricity Can Be Modeled by C C=AertC = A e ^ { r t }C=Aert

The Consumption of Electricity Can Be Modeled by C $C = A e ^ { r t }$