Question

1. the watson family is planting a garden. the cost of getting sod installed for s square feet is given by c(s)=45 + 0.79s. the area of the garden, in square feet, will be determined by the length of the brick - wall, l, they are building to enclose one side of the garden as described by s(l)=l² + 5l for 10 < l < 20. the length l is measured in feet. a. find c(s(12)) and interpret your answer in the context of the problem.

Explanation:

Step1: Find the area when \(l = 12\)

First, use the formula \(S(l)=l^{2}+5l\). Substitute \(l = 12\) into it.
\[S(12)=12^{2}+5\times12=144 + 60=204\]

Step2: Find the cost

Then, use the cost - function \(C(S)=45 + 0.79S\). Substitute \(S = 204\) into it.
\[C(S(12))=C(204)=45+0.79\times204=45 + 161.16=206.16\]

Answer:

\(C(S(12)) = 206.16\). This means that when the length of the brick - wall is 12 feet, the cost of getting the sod installed for the garden is \(206.16\) dollars.