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.

Question

Mahoney

Mathematics

4 March, 15:17

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.

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Moises Pierce · 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.