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) = 3000(t+2), 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 S (Simplify your answer.)

Answer 1

i).
`\$ 7500`

ii).
`\$ 67500`

Explanation:

Given in the question-

Saving rate is s(t)= 3000(t+2)

We know that savings in the 1st year can be calculated as

`\int_(0)^(1)3000(t+2).dt`

`3000\left [ (t^(2))/(2)+2t \right ]_0^1`

`3000\left [ (1)/(2)+2 \right ]`

=
`\$ 7500`

So savings in the first 5 years can be calculated as

`\int_(0)^(5)3000(t+2).dt`

`3000\left [ (t^(2))/(2)+2t \right ]_0^5`

`3000\left [ (25)/(2)+5 \right ]`

=
`\$ 67500`