Answer
f(x) = 190(1.15)x
Explanation
To solve this, we are going to use the standard exponential function:
[tex]f(x)=a(1+b)^x[/tex]
Where
[tex]f(x)[/tex] is the final price after [tex]x[/tex] years
[tex]a[/tex] is the initial price
[tex]b[/tex] is the rate in decimal form
[tex]x[/tex] is the time in years
We know from our problem that the initial price is $190, so [tex]a=190[/tex]. Now to convert the rate, 15%, to decimal form, we are going to divide it by 100%, so [tex]r=\frac{15}{100} =0.15[/tex]. Let's replace the values:
[tex]f(x)=a(1+b)^x[/tex]
[tex]f(x)=190(1+0.15)^x[/tex]
[tex]f(x)=190(1.15)^x[/tex]
