Question

A high-altitude spherical weather balloon expands as it rises, due to the drop in atmospheric pressure. Suppose that the radius r increases at the rate of 0.07 inches per second, and that r = 36 inches at time t = 0. Determine the equation that models the volume V of the balloon at time t, and find the volume when t = 400 seconds.

Answer 1

The increase of the radius is a linear increase since we have the constant rate of 0.07 inches per second

The equation for a linear growth/decay is given by the form
`y=mx+c` where
`m` is the rate of increase and
`c` is the value of
`y` when
`x=0`

We have

`m = 0.07`

`c=36` when
`t=0`

So the equation is
`r=0.07t+36`

The length of the radius when
`t=400` seconds is

`r=0.07(400)+36`

`r=64` inches