# Thread: instantaneous rate word problem

1. ## instantaneous rate word problem

So I was able to do the first part (hopefully it's right), but I'm having trouble trying to figure out what it's asking in the last parts. Here's my problem:

A business is prospering in such a way that its total (accumulated) profit after t years is $\displaystyle 1000t^2$ dollars.

a) How much did the business make during the third year?
so, $\displaystyle f(3)=1000(3)^2=9000$ hopefully its right.

b) What was its average rate of profit during the first half of the third year, between t=2 and t=2.5?

c) What was its instantaneous rate of profit at t=2?

Do I plug in the values for t in part b and c or is there something else invovled? Any help is greatly appreciated!

2. Originally Posted by ascendancy523

b) What was its average rate of profit during the first half of the third year, between t=2 and t=2.5?
$\displaystyle \frac{f(2.5)-f(2)}{2.5-2}$

Originally Posted by ascendancy523

c) What was its instantaneous rate of profit at t=2?
$\displaystyle f'(2)$