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) 18.94 yr
B) 1.89 yr
C) 51.72 yr
D) 0.19 yr

Question

Quizplus · Accepted Answer

Let "t" be the number of years before electricity consumption has tripled.
Using continuous compounding, we have the formula:
A = Pe^(rt)
where A is the final amount, P is the initial amount, r is the annual growth rate (as a decimal), and t is the time in years.
In our case, we want to find "t" when the final amount is three times the initial amount, so we have:
3P = Pe^(0.058t)
Dividing both sides by P, we get:
3 = e^(0.058t)
Taking the natural logarithm of both sides, we have:
ln(3) = 0.058t
Solving for t, we get:
t = ln(3)/0.058 ≈ 18.94 years
Therefore, the answer is A) 18.94 yr.

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