Question

Let f(t) be the weight (in grams) of a solid sitting in a beaker of water. Suppose that the solid dissolves in such a way that the rate of change (in grams/minute) of the weight of the solid at any time t can be determined from the weight using the formula: f'(t)=-4f(t)(3+f(t))

If there is 1 grams of solid at time t=2 estimate the amount of solid 1 second later.

Answer 1

This differential equation is separable:
\[\begin{align*}
\frac{\mathrm{d}f(t)}{\mathrm{d}t}&=-4f(t)(3+f(t))\\\\
\frac{\mathrm{d}f(t)}{f(t)(3+f(t))}&=-4\,\mathrm{d}t
\end{align*}\]