Respuesta :
SOLUTION
The price of the car = $12,000
The depreciate by 10%
[tex]\begin{gathered} \text{ The depreciating value for the first year } \\ 12,000\times(\frac{10}{100})^1 \\ \text{Then} \\ 12,000\times0.1 \end{gathered}[/tex]Then
[tex]12,000-12,00(0.1)[/tex]Then
[tex]\begin{gathered} 12000(1-0.1) \\ 12,000(0.9) \end{gathered}[/tex]For the first year the depreciating value will be
[tex]12,000(0.9)[/tex]Base on the number of years, the exponential equation will be
[tex]\begin{gathered} f(x)=12,000(0.9)^x \\ \text{where } \\ x=\text{ number of years } \end{gathered}[/tex]Therefore
The exponential equation that represent the value of the car is
F(x)=12,000(0.9)^x
The price of the car in 5 yeras will be obtain by substituting x=5 into the equation above
[tex]\begin{gathered} f(x)=12,000(0.9)^x \\ \text{where x=5} \\ f(x)=12,000(0.9)^5=7085.88 \end{gathered}[/tex]The car will worth $7085.88 after 5 years
Similarly, The for 12 years we have x=12
[tex]f(x)=12,000(0.9)^{12}=3389.15[/tex]The car will worth $3389.15 after 12 years
