Question

The botanist would like to increase the number of plants that the environment can support so that the population of the species will increase more rapidly. If the botanists goal is that the number of plants will increase from $3000$ this year to $3360$ next year, how many plants must the modified environment support?

Answer 1

Substituting $N_{\text{thisyear}}=3000$
and $N_{\text{nextyear}}=3360$ in the given equation, we get
$3360=3000+0.2\left(3000\right)(1-\frac{3000}{K})$
$\Rightarrow 360=600(1-\frac{3000}{K})$
$\Rightarrow \frac{360}{600}=1-\frac{3000}{K}$
$\Rightarrow \frac{3}{5}=1-\frac{3000}{K}$
$\Rightarrow \frac{3000}{K}=\frac{2}{5}$
$\Rightarrow K=7500$