Answer:
Explanation:
Assuming that "f" represents the value of the car as a function of time in months, we can use the formula for exponential decay to calculate the value of the car at different times:
f(t) = initial value x (1 - decay rate)^time
In this case, the initial value is $36,900, and the decay rate is 21% per year, which is equivalent to 1.75% per month (since there are 12 months in a year). Therefore, the decay rate can be expressed as 0.0175.
To calculate the value of the car after a certain number of months, we can substitute the time (in months) into the formula for f(t). For example:
At f(1) month:
f(1) = $36,900 x (1 - 0.0175)^1 = $36,209.63
So the value of the car after 1 month of depreciation is approximately $36,209.63.
At f(6) months:
f(6) = $36,900 x (1 - 0.0175)^6 = $31,573.13
So the value of the car after 6 months of depreciation is approximately $31,573.13.
At f(8) months:
f(8) = $36,900 x (1 - 0.0175)^8 = $29,784.62
So the value of the car after 8 months of depreciation is approximately $29,784.62.
Note that these calculations are based on the assumption that the depreciation rate remains constant over time. In reality, the depreciation rate may change due to various factors, such as wear and tear, market conditions, and maintenance. Therefore, these values should be considered as estimates only.