Answer:
The value of car after n years at the depreciation rate is $ 50,000 [tex](0.9)^{n}[/tex] .
Step-by-step 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 × [tex](1 - \dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, $ A = $50,000 × [tex](1 - \dfrac{\textrm r}{100})^{\textrm n}[/tex]
Or, $ A = $50,000 × [tex](1 - \dfrac{\textrm 10}{100})^{\textrm n}[/tex]
Or, $ A = $50,000 × [tex](\frac{90}{100})^{n}[/tex]
I.e $ A = $50,000 × [tex](0.9)^{n}[/tex]
So, value of car after n years = $ 50,000 [tex](0.9)^{n}[/tex]
Hence The value of car after n years at the depreciation rate is $ 50,000 [tex](0.9)^{n}[/tex] . Answer
