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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.

Respuesta :

merlynthewhizz
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

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