Given :
Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%.
Its current value is $2,000.
To Find :
Age of car.
Solution :
Price of car after 1 year :
[tex]P_1=P_o(1-0.35)[/tex]
Price of car after 2 year :
[tex]P_2=P_1(1-0.35)\\\\P_2=[P_o(1-0.35)](1-0.35)\\\\P_2=P_o(1-0.35)^2[/tex]
So, price of car after n years.
[tex]P_n=P_o(1-0.35)^n[/tex]
[tex]2000=16000(1-0.35)^n\\\\0.65^n=0.125\\\\n\times log(0.56)=log(0.125)\\\\n=\dfrac{log(0.125)}{log(0.56)}\\\\n=3.58[/tex]
Therefore, age of car in nearest whole number is 4 years.
Hence, this is the required solution.
