Question

Jill bought a car for $50,000. Her car depreciates at a rate of 10% a year. create an equation for the problem

Answer 1

The value of car after n years at the depreciation rate is $ 50,000
`(0.9)^(n)` .

Explanation:

Given as :

The cost of the car that Jill bought = $ 50,000

The depreciation rate of car value = r = 10 % a years

Let The car after n years of depreciation = $ A

Now, According to question

The cost of car after n years of depreciation = initial cost of car ×
`(1 - (\textrm rate)/(100))^(\textrm time)`

Or, $ A = $50,000 ×
`(1 - (\textrm r)/(100))^(\textrm n)`

Or, $ A = $50,000 ×
`(1 - (\textrm 10)/(100))^(\textrm n)`

Or, $ A = $50,000 ×
`((90)/(100))^(n)`

I.e $ A = $50,000 ×
`(0.9)^(n)`

So, value of car after n years = $ 50,000
`(0.9)^(n)`

Hence The value of car after n years at the depreciation rate is $ 50,000
`(0.9)^(n)` . Answer