<p>The rate of growth of the volume of a sphere is poroportional to its volume. If the volume of the sphere is initially 36pi ft^3, and expands to 90 pi ft^3, find the volume of the sphere after 3 seconds. Thanks</p>
<p>PS: Anyone has the solutions to the 1992 Physics free response and 1993 M/C? Willing to trade, thanks.</p>
<p>I think that this is just an exponential growth problem, but I don't know since there doesn't seem to be any time frame for the expansion from 36pi to 90pi.</p>
<p>If dV/dt is proportional to the volume, dV/dt=kV. Rearranging, you get dV/V = k(dt). Integrating yields ln(V) = kt + C or V = e^(kt+C). Use the rules about exponent multiplication to get V = (e^C)(e^(kt)). Since V(0) = 36, e^c = 36. If you know how long the expansion from 36pi to 90pi takes, you can solve for k by using 90=36e^(kt). I don't know if that was helpful or not; sorry.</p>
<p>thanks :)</p>
the question is missing the time frame for the 90pi volume.
v(0) = 36pi
v(1) = 90pi
v(3) = ???
The way you would solve it is the way sl8r000 did +
after you’ve gotten v = e^(kt+c), you plug in v(0) = 36pi and v(1) = 90pi to find k and c.
Then, you end up with the equation v = 36pi e^0.916t. Now, you can substitute t = 3 and you get 1767 or approximately 1800 ft^3.
The question was posed 8 years ago. I think they figured out the answer by now. Please do not resurrect old threads. Closing.