Question

4. Suppose a Tesla's value depreciates by 12% each year. If the initial value of the Tesia was $58,000,

how many MONTHS will it take for the Tesia to be valued at 28,000. Round to the nearest whole month.

Please explain, thank u so much!

Answer 1

It will take 57 months

Explanation:

We can use the following formula to calculate the value of the Tesla after a certain number of years of depreciation:

V = P(1 - r/100)^n

where V is the value of the Tesla after n years of depreciation, P is the initial value of the Tesla, r is the depreciation rate per year, and n is the number of years of depreciation.

In this case, P = $58,000, r = 12%, and we want to find the value of n in months when V = $28,000.

So we can write:

$28,000 = $58,000(1 - 12/100)^(n/12)

Simplifying this equation:

0.48^(n/12) = 0.4828

Taking the logarithm of both sides with base 0.48:

(n/12) log(0.48) = log(0.4828)

n/12 = log(0.4828) / log(0.48)

n = 12 * (log(0.4828) / log(0.48))

n ≈ 56.7 months

Rounding to the nearest whole month, it will take 57 months for the Tesla to be valued at $28,000.