Question
you paid $32,500 for a new car, but it depreciates at an 8% rate every year. What would be the function equation ( f(x) )? and how much is your car worth after 5 years?
Answers
GPT 3.5
To find the value of the car after each year, we can use the formula for exponential decay:
f(x) = $32,500 * (1 - 0.08)^x
Where:
- f(x) is the value of the car after x years
- $32,500 is the initial value
- 0.08 is the depreciation rate
- x is the number of years
To find the value after 5 years:
f(5) = $32,500 * (1 - 0.08)^5
f(5) = $32,500 * (0.92)^5
f(5) = $32,500 * 0.681472
f(5) ≈ $22,173.06
So, the car would be worth approximately $22,173.06 after 5 years.
f(x) = $32,500 * (1 - 0.08)^x
Where:
- f(x) is the value of the car after x years
- $32,500 is the initial value
- 0.08 is the depreciation rate
- x is the number of years
To find the value after 5 years:
f(5) = $32,500 * (1 - 0.08)^5
f(5) = $32,500 * (0.92)^5
f(5) = $32,500 * 0.681472
f(5) ≈ $22,173.06
So, the car would be worth approximately $22,173.06 after 5 years.