Question

after a new firm starts in business, it finds that its rate of profits after t years of operation is given by dP/dt=3t^2+10t+8. find the profit in year 7 of the operation

Answer 1

Is there no other initial information? You can integrate that to get P(t), but that'll include an arbitrary +C constant.

Answer 2

I suppose you can assume P=0 at t=0?

Answer 3

yes

Answer 4

Ok, do you know how to integrate polynomials?

Answer 5

yes I do I get t^3+5t^2+8t

Answer 6

Ok, then with the assumption that P(0)=0, find P(7).

Answer 7

I did but I get 833 but the answer is 20,000 dont know how

Answer 8

20,000? Are you sure there isn't any other information?
How did you get 833? I did what I think you did and got 644.

Answer 9

yupe thats all I have as info

Answer 10

*scratches head* ermmm . . . I don't know then.
If dP/dt = 3t^2+10t+8 then P(t)=t^3+5t^2+8t assuming P(0)=0.
P(7) = (7)^3+5(7)^2+8(7) = 644.

I have no idea how a 20,000 could come out of that.

Answer 11

thanks :((