Chapter 11.3, Problem 33E

Immigration An island is colonized by immigration from the mainland, where there are 100 species. Let the number of species on the island at time t (in years) equal y, where $y=f\left(t\right)$. Suppose the rate at which new species immigrate to the island is

$\frac{dy}{dx}=0.02\left(100-y^{\frac{1}{2}}\right)$

Use Euler’s method with $h=0.5$ to approximate y when $t=5$ if there were 10 species initially.