Question

Asap!! step by step pls! After a new firm starts in business, it finds that it’s rate of profit (in hundreds of dollars) after t years of operations is given by P’(t)=3t^2+10t+6. Find the profit in year 4 of the operation.

Answer 1

$ 7800

Explanation:

P'(t) = 3t² + 10t + 6

`P(t) = \int\limits^a_b {P'(t)} \, dt`

For the 4th year, the limits are [3,4]

`P(t) = \int\limits^4_3 {3t^2 + 10t + 6} \, dt\\\\= [(3t^3)/(3) + (10t^2)/(2) + 6t]^(^4)__(3)\\\\`

`=[(3(4)^3)/(3) + (10(4)^2)/(2) + 6(4)]-[(3(3)^3)/(3) + (10(3)^2)/(2) + 6(3)]\\\\=[(3(64))/(3) + (10(16))/(2) + 24]-[(3(27))/(3) + (10(9))/(2) + 18]\\\\= [64 + 5(16) + 24]-[27+5(9) + 18]\\\\= 168-90\\\\= 78`

= $ 7800