Math Question
![31. Business: Savings Realized from New Equipment A company can save money by buying new equipment, but at the same time will have to spend money to maintain it. The savings realized by the new equipment are
\[
S(t)=3.6 t+8
\]
and the cost of maintaining the equipment is
\[
C(t)=4.8 t
\]
where \( t \) is the number of years since the purchase of the equipment and \( S(t) \) and \( C(t) \) are in thousands of dollars. Find the area between the curves \( S(t) \) and \( C(t) \) and interpret the result. (Hint: To find the area you need to establish the limits of integration. Determine where the curves intersect by solving the equation \( S(t)=C(t) \).)](https://d3hlidq5bf9vg0.cloudfront.net/app-server-student/2022/4/27/552e6809-ad7f-4590-8794-166d018fa532.png "31. Business: Savings Realized from New Equipment A company can save money by buying new equipment, but at the same time will have to spend money to maintain it. The savings realized by the new equipment are
\[
S(t)=3.6 t+8
\]
and the cost of maintaining the equipment is
\[
C(t)=4.8 t
\]
where \( t \) is the number of years since the purchase of the equipment and \( S(t) \) and \( C(t) \) are in thousands of dollars. Find the area between the curves \( S(t) \) and \( C(t) \) and interpret the result. (Hint: To find the area you need to establish the limits of integration. Determine where the curves intersect by solving the equation \( S(t)=C(t) \).)")
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