Answer:
The first option f(x) = 25,399(0.915)^x
Explanation:
The price of the vehicle decreases by 8.5% per year. Therefore, after each consecutive year, the price of the vehicle is 100% - 8.5% = 91.5% of the price the previous year.
Now if the price at the beginning is $25,399, then the price after one year will be 91.5% of $25,399.
[tex]price\text{ in the first year}$ =25,399 $\times\frac{91.5}{100}[/tex]
The price after two years then will be
[tex]price\text{ in the second year}=price\text{ in the first year }\times\frac{91.5}{100}[/tex][tex]\Rightarrow price\text{ in the second year}=25,399\times\frac{91.5}{100}\times\frac{91.5}{100}[/tex]
The price after the 3 years then is 91.5% of the price in the second year:
[tex]25,399\times\frac{91.5}{100}\times\frac{91.5}{100}\times\frac{91.5}{100}[/tex]
Note that for the first year we multiplied $25,399 by 91.5/100 once, in the second year we multiplied by it twice, and in the third year we multiplied thrice. Therefore, We see a pattern here. The price after x years is $25,399 multiplied by 91.5/100 x times.
In other words, after xth year the price of the vehicle will be
[tex]25,399\times(\frac{91.5}{100})^x[/tex]
Since 91.5/100 = 0.915, the above becomes
[tex]25,399(0.915)^x[/tex]
If we represent this price by f(x) then we have
[tex]\boxed{f\mleft(x\mright)=25,399\left(0.915\right)^x.}[/tex]
