Answer
f(x) = 6(1.09)x + 3
Explanation
To find our exponential equation, we are going to complete the standard exponential growth equation:
[tex]f(x)=a(1+b)^x[/tex]
where
[tex]a[/tex] is the initial quantity
[tex]b[/tex] is the growth rate in decimal form
[tex]x[/tex] is the time (in months for our model)
Since the hours of classical music remain constant, we just need to add them at the end of our calculations.
We know that Wendy initially has 6 hours of pop music, so [tex]a=6[/tex]. We also know that he hours of pop music in her collection is 9% more than what she had the previous month, so [tex]b=\frac{9}{100} =0.09[/tex]. Let's replace the values in our function:
[tex]f(x)=a(1+b)^x[/tex]
[tex]f(x)=6(1+0.09)^x[/tex]
[tex]f(x)=6(1.09)^x[/tex]
Now we just need to add the hours of classical music to complete our model:
[tex]f(x)=6(1.09)^x+3[/tex]
