Question

A new car worth $20,000 loses 20% of its value every year. Is the value of the car represented by a linear or exponential function?

Answer 1

Exponential Function
`y = $20,000(0.8)^x`
where `x` = time

Explanation:

Exponential function:
`y = a(b)^x`

`a` = principal value
`b` = rate (growth or decay)
`x` = time

Since the initial value (principal amount) is $20,000 it needs to represent the `a` value. The rate would be a decay since it is losing 20% of its value every year (`1 - 0.2 = 0.8`). The time is in year. So it is: `y = $20,000(0.8)^x`