Question

Wendy enjoys listening to hip hop and downloads music regularly from the internet. She already has four hours of hip hop in her collection. From the second month onward, the number of hours of hip hop music she downloads each month is nine percent greater than the number of hours of hip hop music she had downloaded the previous month. Which function best shows the total number of hours of hip hop music Wendy has in her collection f(x) after x months? f(x) = (1.09)x + 3 f(x) = 3(1.09)x f(x) = (1.09)x + 2 f(x) = (1.09)x - 2

Answer 1

This can be solved using a geometric sequence. 
First term $u_1=4$ also, $u_{n+1}=u_n+0.09u_n=1.09u_n$.
Let x be the number of months, then the total number of hours can be computed like this:
$f(x)=4\dfrac{1-1.09^x}{1-1.09}\\=44.4(1-1.09^x)$