# Science:Math Exam Resources/Courses/MATH103/April 2010/Question 06 (b)

MATH103 April 2010
Other MATH103 Exams

### Question 06 (b)

The height of fluid, ${\displaystyle h(t)}$ in a cylindrical container is controlled by a pump so that it satisfies the differential equation

${\displaystyle {\frac {dh}{dt}}=-kh^{1/3},\quad h(0)=h_{0}}$

where ${\displaystyle k>0}$, ${\displaystyle h_{0}>0}$ are constants, and ${\displaystyle h_{0}}$ is the initial height of the fluid.

(b) At what time will the container be empty?

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