Question

Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10%. The second car depreciates at an annual rate of 15%. What is the approximate difference in the ages of the two cars?

1.7 years
2.0 years
3.1 years
5.0 years

Answer 1

Answer is A - 1.7

Explanation:

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Answer 2

Answer: 1

Explanation:

Let the original price of first car = x dollars,

If after t years the price of car by decreasing 10% per year = 60 % of the original price = 60 % of x = 0.6 x

Hence, For first car,

`0.6x = x (1-(10)/(100))^(t_1)`

`\implies 0.6 = (1-0.1)^(t_1)`

`\implies 0.6 = 0.9^(t_1)`

By taking log on both sides,

`\implies log(0.6) = t_1 log(0.9)`

`t_1=(log(0.6))/(log(0.9))=4.84835918443\approx 4.85`

Now,

Let the original price of second car = y dollars,

If after t years the price of car by decreasing 15% per year = 60 % of the original price = 60 % of y = 0.6 y

Hence, For second car,

`0.6x = x (1-(15)/(100))^(t_2)`

`\implies 0.6 = (1-0.15)^(t_2)`

`\implies 0.6 = 0.85^(t_2)`

By taking log on both sides,

`\implies log(0.6) = t_2 log(0.85)`

`t_2=(log(0.6))/(log(0.85))=3.14317615397\approx 3.14`

Hence, the difference in the ages of the two cars = 4.85 - 3.14=1.71 years.

Thus, the difference in the ages of the two cars is approximately 1 years.