Question

Assume the cost of a car is $25,000. With continuous compounding, in effect, the cost of the care will increase according to the equation C=25,000e^et, 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 rate at an annual inflation of 3.2%. Round the answer to the nearest hundredth.

Answer 1

The value of t that makes the factor e^(.032t) have the value of 2 can be found using logarithms.
2 = e^(0.032t)
ln(2) = ln(e^(0.032t)) = 0.032t
t = ln(2)/0.032 ≈ 21.66

It would take 21.66 years for the cost to double.