Maths
posted by Lucy on .
As water drains out of a 2000L hot tub, the amount of water remaining in the tub can be modelled by the function V=0.00002(100t)^4 , where t is the time, in minutes (t is greater than or equal to 0 and less than or equal to 100), and V is the volume of water, in litres, remaining in the tub at time t.
Determine the average rate of cahnge of the volume of water during
 the entire 100 min
 the first 30 min
 the last 30 min
I'm really confused as to what I actually have to do. I'd really appreciate some help.

I believe what you are asked to do is something like this.
For the 100 min period
V=0.00002(100100)^4 = 0 L remaining.
So all 2000 L have drained; therefore, the rate of change is 2000L/100 min = 20L/min.
For the first 30 min
V=0.00002(10030)^4 = 480.2 L remaining or 2000480.2 =1519.8 L drained.
rate of change is 1519.8/30 = 50.7 L/min.
Etc. Check my thinking. Check my work. 
oh okay, thank you.