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