# Thread: Calculus Average & Instantaneous Change?

1. ## Calculus Average & Instantaneous Change?

A weather balloon that contains 540m^3 of helium springs a leak and empties in 60 seconds. Suppose that the volume of helium in the balloon as a function of time is given by V(t)=540(1-t/60)^3.

Find:

a) the average rate of change of volume during the 60 seconds it takes to empty.

b) the volume of the balloon after 40 seconds.

c) the instantaneous rate of change of the volume at 40 seconds.

I'm not sure where to start, if I'm not mistaken to find the average rate of change you find the first derivative, to find the instantaneous rate of change you find the second derivative.

2. Originally Posted by lionpants
A weather balloon that contains 540m^3 of helium springs a leak and empties in 60 seconds. Suppose that the volume of helium in the balloon as a function of time is given by V(t)=540(1-t/60)^3.

Find:

a) the average rate of change of volume during the 60 seconds it takes to empty.

b) the volume of the balloon after 40 seconds.

c) the instantaneous rate of change of the volume at 40 seconds.

I'm not sure where to start, if I'm not mistaken to find the average rate of change you find the first derivative, to find the instantaneous rate of change you find the second derivative.
The average rate of change is the initial value minus the end value divided by the time for the change.

The instantaneous rate of change is the derivative.

RonL