Final answer:
The installation fee for carpet is modeled by the function g(x) = 0.375x + 100, which includes 5% of the carpet cost plus an additional $100. For 150 square feet of carpet, the installation fee would be $156.25.
Step-by-step explanation:
The installation fee for carpet can be represented by a function g(x), where x represents the number of square feet of carpet. The total cost of the carpet is given by the function f(x) = 7.5x. The installation fee is $100 more than 5% of the cost of the carpet, so we can express g(x) as g(x) = 0.05f(x) + 100.
Substituting f(x) into g(x) gives:
g(x) = 0.05(7.5x) + 100
Simplifying this, we get:
g(x) = 0.375x + 100
To find the installation fee for 150 square feet of carpet, we substitute x = 150 into g(x):
g(150) = 0.375(150) + 100
This gives us:
g(150) = 56.25 + 100
g(150) = $156.25
So the installation fee for 150 square feet of carpet is $156.25.