a little calculus?

Question

So i have a calculus problem that I am having a bit of trouble with. For rendering purposes i made the problem into a picture on imageshack. Here is the link:
http://img111.imageshack.us/img111/4306/pow2wv7.jpg
Thanks in advance for your help!!

Answer 1

a). There are lots of ways to approximate W'(12). Here's a simple approximation:
W'(12) ≈ (W(15) - W(9)) / (15 - 9) = -3/6 = -0.5deg;C/day.

b). Average temp ≈ (1/2 W(0) + W(3) + W(6) + W(9) + W(12) + 1/2 W(15) / 5 = (10 + 31 + 28 + 24 + 22 + 10.5) / 5 = 25.1°C.

c). P(t) = 20 + 10 t e^(-t/3)
=> P'(t) = 10 e^(-t/3) + 10 t e^(-t/3) (-1/3)
= 10 e^(-t/3) (1 - t/3)
So P'(12) = 10 e^(-4) (1 - 4) = -30 e^(-4) = -0.55°C/day.

d). It means that, in the proposed model, the water temperature is declining at a rate of 0.55°C per day after 12 days.