Problem 1
<h3>Answer: Choice C) 1/2</h3>
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Explanation:
Let's plug 8 into f(x)

Repeat for g(x)

I used the change of base formula in the third step.
Lastly, we subtract the results like so

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Problem 2
<h3>Answer: Choice A) 8</h3>
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Explanation:
Through trial and error (I recommend the rational root theorem), you should find that the roots of R(x) are: -1, 3, and 8
We'll only focus on positive x values. So we focus on the roots 3 and 8.
It turns out that the R(x) curve dips below the x axis when x is between 3 and 8. When x > 8 is when R(x) is positive and goes upward forever. This represents when the company is making money.
The company does make money when x is between 0 and 3; however, this is a short timespan compared to the other interval. So it's much more effective and realistic to say that the company makes money after 8 days.
In other words, yes the company makes money between day 0 and day 3, but from day 3 to day 8 is when the company loses money. Ultimately the company is profitable again when it's beyond day 8.