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

1

Step-by-step 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,

By taking log on both sides,

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,

By taking log on both sides,

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.