The volume of water remaining in a hot tub when it is being drained satisfies the differential equation
dV/dt = −2 ( V)^(1/2)
, where V is the number of cubic feet of water that remain t minutes after the drain is opened. Find V if the tub initially contained 121 cubic feet of water.

Question

The volume of water remaining in a hot tub when it is being drained satisfies the differential equation
 dV/dt = −2 ( V)^(1/2) 
, where V is the number of cubic feet of water that remain t minutes after the drain is opened. Find V if the tub initially contained 121 cubic feet of water.

anonymous · Answer

First separate variables and solve the differential equation for V

anonymous · Answer

$$dV/V ^{1/2} = -2dt$$

anonymous · Answer

so
$$\int\limits_{?}^{?}dV/V ^{1/2} = \int\limits_{?}^{?} -2dt$$

anonymous · Answer

where both of those are indefinite integrals

anonymous · Answer

alright great! I've got it from there! Thank you very much.

anonymous · Answer

No problem, let me know if you get stuck anywhere else with this one

anonymous · Answer

$$V = t ^{2}-22t+121$$ was the final answer i found

anonymous · Answer

yes i did too except i left it as (-t+11)^2

anonymous · Answer

perfect :)

anonymous · Answer

thanks again!