Calculus Time Interval Problem

[Bluewolf1986]

Hello, please help with this problem I am stuck on: At what average rate is the volume of an oil tank leaking during the 301st minute (that is, between the interval of 300 and 301 minutes) in liters per hour? The function of the volume of the tank with respect to time (hours) is 2(10-t)^5/2. I tried to use linear approximation using the average rate of 5 hours (-104.13 L/hr.) with the formula f(a)+f'(a)(x-a) but I didn't get the right answer. Help would be much appreciated for this, thank you.

 

[Dr.Peterson]

They're asking, not for a linear approximation (via a tangent), but for the average rate (the slope of a secant line).

Just find the amount leaked from t=300 to t=301 (in liters), and divide by the time (in hours). Use actual values of the function. (No calculus.)

 

[Bluewolf1986]

Great, thanks! The wording of the problem was what confused me about it. I appreciate you making it seem clear and explaining how to solve it!