Question

Sue initially has 5 hours of pop music and 4 hours of classical music in her collection. Every month onwards, the hours of pop music in her collection is 25% 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?a. f(x) = 4(1.25)x + 5
b. f(x) = 5(1.25)x + 4
c. f(x) = 4(0.25)x + 5
d. f(x) = 5(0.25)x + 4

Answer 1

Answer

f(x) = 5(1.25)x + 4

Explanation

To solve this, we are going to use the standard exponential equation:

$f(x)=a(1+b)^x$

where

$a$ is the initial amount

$b$ is the growth rate in decimal form

$x$ is the time (in months for our case)

Since the hours of classic music remain constant, we just need to add them at the end. We know form our problem that Sue initially has 5 hours of pop, so $a=5$; we also know that every month onward, the hours of pop music in her collection is 25% more than what she had the previous month, so $b=\frac{25}{100} =0.25$. Now let's replace the values in our function:

$f(x)=a(1+b)^x$

$f(x)=5(1+0.25)^x$

$f(x)=5(1.25)^x$

Now we can add the hours of classical music to complete our function:

$f(x)=5(1.25)^x+5$

Answer 2

It isn't A because if it was Pop music that doesn't change, it would be in the end of the equation. Because if you multiply the 1.25 by classical, that means it changes to a different number other than 4. But it can't change. Pop can then.

It is B. f(x)=5(1.15)^x+4. Hope this helps!