Question

A company is considering a new manufacturing process. It knows that the rate of savings (in dollars per year) from the process will be about S(t) = 5000(t + 3), where t is the number of years the process has been in use. Find the total savings during the first year. Find the total savings during the first 5 years. The total savings during the first year is __________

Answer 1

Total saving during first 5 years=$137500

Total saving during first year=$17500

Explanation:

We are given that

Savings rate

`S(t)=5000(t+3)`

Total saving during first 5 years is given by

`=\int_(0)^(5)5000(t+3)dt=5000[(t^2)/(2)+3t)]^(5)_(0)`

Total saving during first 5 years=
`5000((25)/(2)+3(5))`=$137500

Total saving during first year=
`\int_(0)^(1)5000(t+3)dt`

Total saving during first year=
`5000[((t^2)/(2)+3t)]^(1)_(0)`

Total saving during first year=
`5000((1)/(2)+3)=`$17500