A spherical raindrop increases in volume, $V$, at a constant rate of $450\pi {mm}^3{min}^{-1}$ as it falls through a mist. Calculate the rate at which the radius, $r$, is increasing in ${mm\; min}^{-1}$ at the moment when $r=15mm$. [The volume $V$ of a sphere of radius $r$ is given by the formula $V=\frac{4}{3}\pi r^3$]

The mass, $Mgrams$, of a crystal growing in a saturated solution is monitored over time. The rate of increase in the mass of the crystal is modeled by the differential equation

where $k$ is a positive constant and $t$ hours is the time after monitoring began. Given that:

• initially (at $t=0$), the mass of the crystal was $4grams$.
• $10$ hours after monitoring began, the mass of the crystal was $9grams$.
• $T$ hours after monitoring began, the mass of the crystal was $25grams$.

Solve the differential equation to find the value of $T$. Give your answer to one decimal place.