Albert buys a car for $12,000. The value of the car depreciates about 9% per year. After about how many years will the car be worth $7500?

Answer:[tex]5\ years[/tex]  Step-by-step explanation:we know that The  formula to calculate the depreciated value  is equal to   [tex]D=P(1-r)^{t}[/tex]  where   D is the depreciated value   P is the original value   r is the rate of depreciation  in decimal  t  is Number of Time Periods   in this problem we have   [tex]P=\$12,000\\r=9\%=0.09\\D=\$7,500[/tex] substitute in the formula above and solve for t[tex]\$7,500=\$12,000(1-0.09)^{t}[/tex]  [tex](7,500/12,000)=(0.91)^{t}[/tex]  Apply log both sides[tex]log(7,500/12,000)=t*log(0.91)[/tex]  [tex]t=log(7,500/12,000)/log(0.91)=5\ years[/tex]