Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10%. The

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?
A. 1.7 years
B. 2.0 years
C. 3.1 years
D. 5.0 years​

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Aaliyah 2 weeks 2021-09-10T13:01:46+00:00 2 Answers 0

Answers ( )

    0
    2021-09-10T13:03:08+00:00

    Answer: A) 1.7 Years

    Step-by-step explanation:

    0
    2021-09-10T13:03:42+00:00

    Answer:

    A. 1.7 years

    Step-by-step explanation:

    Let P_1 be the original value of first car,

    Since, the car depreciates at an annual rate of  10%,

    Let after t_1 years the value of car is depreciated to 60%,

    That is,

    P_1(1-\frac{10}{100})^{t_1}=60\%\text{ of }P_1

    P_1(1-0.1)^{t_1}=0.6P_1

    0.9^{t_1}=0.6

    Taking ln on both sides,

    t_1ln(0.9) = ln(0.6)

    \implies t_1=\frac{ln(0.6)}{ln(0.9)}

    Now, let P_2 is the original value of second car,

    Since, the car depreciates at an annual rate of 15%

    Suppose after t_2 years it is depreciated to 60%,

    P_2(1-\frac{15}{100})^{t_2}=60\%\text{ of }P_2

    P_2(1-0.15)^{t_2}=0.6P_2

    0.85^{t_2}=0.6

    Taking ln on both sides,

    t_2ln(0.85) = ln(0.6)

    \implies t_2=\frac{ln(0.6)}{ln(0.85)}

    \because t_1-t_2=\frac{ln(0.6)}{ln(0.90)}-\frac{ln(0.6)}{ln(0.85)}

    =1.70518303046

    \approx 1.7

    Hence, the approximate difference in the ages of the two cars is 1.7 years,

    Option ‘A’ is correct.

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