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.
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 [tex]y=mx+c[/tex] where [tex]m[/tex] is the rate of increase and [tex]c[/tex] is the value of [tex]y[/tex] when [tex]x=0[/tex]
We have [tex]m = 0.07[/tex] [tex]c=36[/tex] when [tex]t=0[/tex]
So the equation is [tex]r=0.07t+36[/tex]
The length of the radius when [tex]t=400 [/tex] seconds is [tex]r=0.07(400)+36[/tex] [tex]r=64[/tex] inches
