Mathematics: 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

Two different cars each depreciate to 60% of their

selenamr

11.01.2022

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,

$0.6x = x (1-\frac{10}{100})^{t_1}$

$\implies 0.6 = (1-0.1)^{t_1}$

$\implies 0.6 = 0.9^{t_1}$

By taking log on both sides,

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

$t_1=\frac{log(0.6)}{log(0.9)}=4.84835918443\approx 4.85$

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,

$0.6x = x (1-\frac{15}{100})^{t_2}$

$\implies 0.6 = (1-0.15)^{t_2}$

$\implies 0.6 = 0.85^{t_2}$

By taking log on both sides,

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

$t_2=\frac{log(0.6)}{log(0.85)}=3.14317615397\approx 3.14$

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.

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