Question

Wendy initially has 6 hours of pop music and 3 hours of classical music in her collection. Every month onwards, the hours of pop music in her collection increase by 9%. Which function shows the total hours of music she will have in her collection after x months?

A. f(x) = 6 * (1.09)^x + 3
B. f(x) = 3 * (1.09)^x + 6
C. f(x) = 6 * (0.09)^x + 3
D. f(x) = 3 * (0.09)^x + 6

Answer 1

The correct function that shows the total hours of music in Wendy's collection after x months is f(x) = 6 × (1.09)^x + 3, which accounts for the monthly growth rate of 9% for pop music and the constant amount of classical music.

Step-by-step explanation:

The question is about finding the function that represents the total hours of music in Wendy's collection after x months, given that she initially has 6 hours of pop music and 3 hours of classical music and that the hours of pop music increase by 9% each month. The correct function is f(x) = 6 × (1.09)^x + 3, which is option A.

To arrive at this answer, we consider that the hours of pop music (initially 6 hours) are growing at a rate of 9% per month. This growth rate can be represented by multiplying the original amount of pop music by (1.09)^x, with x being the number of months. The 3 hours of classical music in her collection remain unchanged, hence they are simply added to the total without any exponential growth factor.