Meg initially has 3 hours of pop music and 2 hours of classical music in her collection. Every month onwards, the hours of pop music in her collection is 5% more than what she had the previous month. Her classical music does not change. Which function shows the total hours of music she will have in her collection after x months?
f(x) = 2(0.05)^x + 3
f(x) = 3(0.05)^x + 2
f(x) = 2(1.05)^x + 3
f(x) = 3(1.05)^x + 2
is it c
D since it's the pop music that is increasing by 5% not the classical music. The classical music is a constant of 2 plus the increasing pop music.
thx so much!
Yes, you are correct. The function that shows the total hours of music Meg will have in her collection after x months is:
f(x) = 2(1.05)^x + 3
Yes, it is option c. The function that shows the total hours of music Meg will have in her collection after x months is:
f(x) = 2(1.05)^x + 3
Here's how you can determine this:
Since Meg's classical music does not change, we can ignore it. We only need to focus on the hours of pop music.
Starting with 3 hours of pop music, every month the amount increases by 5% more than what she had the previous month. This means that the total hours of pop music can be calculated using the equation:
f(x) = 3 * 1.05^(x-1)
However, notice that in this equation, when x = 1, the exponent would be 0, which would result in 1.05^0 = 1. To adjust for this, we can rewrite the equation as:
f(x) = 3 * 1.05^(x-1) + 2
Simplifying this equation gives us:
f(x) = 2(1.05)^x + 3
Therefore, option c is the correct answer.