Assume the cost of a car is $20,000. With continuous compounding in effect, the cost of the car will increase according to the equation C $C = 20,000 \mathrm { e } ^ { \mathrm { rt } }$ , where r is the annual inflation rate and t is the number of years. Find
The number of years it would take to double the cost of the car at an annual inflation rate of 5.9%. Round the
Answer to the nearest hundredth.
A) 167.86 years
B) 1.68 years
C) 179.60 years
D) 11.75 years

Question

Quizplus · Accepted Answer

To find the number of years it takes for the cost of the car to double at an annual inflation rate of 5.9%, we set $C = 2 \times 20,000 = 40,000$ and solve for $t$ in the equation $40,000 = 20,000 \mathrm{e}^{0.059t}$. Dividing both sides by 20,000 gives $2 = \mathrm{e}^{0.059t}$. Taking the natural logarithm of both sides gives $\ln(2) = 0.059t$, and solving for $t$ gives $t = \frac{\ln(2)}{0.059}$, which approximately equals 11.75 years.

Assume the Cost of a Car Is $20,000 C=20,000ertC = 20,000 \mathrm { e } ^ { \mathrm { rt } }C=20,000ert

Assume the Cost of a Car Is $20,000 $C = 20,000 \mathrm { e } ^ { \mathrm { rt } }$