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

Answer:

i). $\ 7500$

ii).$\ 67500$

Step-by-step 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

    $\int_{0}^{1}3000(t+2).dt$

    $3000\left [ \frac{t^{2}}{2}+2t \right ]_0^1$

    $3000\left [ \frac{1}{2}+2 \right ]$

 = $\ 7500$

So savings in the first 5 years can be calculated as

     $\int_{0}^{5}3000(t+2).dt$

    $3000\left [ \frac{t^{2}}{2}+2t \right ]_0^5$

    $3000\left [ \frac{25}{2}+5 \right ]$

 = $\ 67500$