Question

You buy a new car and it depreciates 6.2% per year in value. If the value of the car can be modeled by V(t)=45,000⋅bt, what would be the value of b?

Answer 1

b = 0.938

Explanation:

Value of the car can be modeled by the function,

V(t) =
`45000(b)^t`

Since, formula for the depreciation is modeled by,

V(t) =
`V_0(1-(r)/(100))^t`

Here, V(t) = Final value of the car after t years

V(0) = Initial value of the car

r = rate of depreciation

t = Time (in years)

By comparing both the functions which are similar,

`1-(r)/(100)=b`

`1-(6.2)/(100)=b`

b = 1 - 0.062

b = 0.938