Question

$36000. For every year after it is purchased, the car loses 17% of its value due to depreciation. What is the value of the car after 64 months?

for mah grade 11 answer needed in exponential function well lables
(A) Value of car = $36000 * (1 + 0.17)^Time
(B) Value of car = $36000 * (1 - 0.17)^Time
(C) Value of car = $36000 * (1 - 0.17)^(1 / Time)
(D) Value of car = $36000 * (1 + 0.17)^(1 / Time)

Answer 1

The value of the car after 64 months can be calculated using the formula $36000 * (1 - 0.17)^(Time), with Time being the number of years. Since depreciation is 17% per year, we convert the months into years by using 64/12 for Time in the equation. The correct exponential function to represent this situation is formula (B).

Step-by-step explanation:

The value of a car after a certain period can be determined by using an exponential function to model depreciation. The correct equation to determine the value of the car after 64 months, given that it loses 17% of its value each year due to depreciation, should account for the decrease in value. Since the car is losing value, we must subtract the percentage of depreciation from 1. Additionally, because the time is given in months, we need to convert this time into years, as the depreciation rate is per year. Thus, the equation takes the form of:

Value of car = $36000 * (1 - 0.17)^(Time/12)

Therefore, the correct answer would be:

(B) Value of car = $36000 * (1 - 0.17)^(Time)

But we must substitute Time with 64/12 to convert the months into years. The adjusted formula is:

Value of car = $36000 * (1 - 0.17)^(64/12)