Modeling Species Diversity in Succession

In an ecosystem undergoing succession, the rate of change of species diversity, D, is modeled by the differential equation $\frac{dD}{dt}= k(S_{max}- D)$, which has the solution $D(t)= S_{max} - (S_{max}- D(0))e^{-kt}$. Given an initial diversity, D(0), of 10 species, a maximum diversity, $S_{max}$, of 50 species, and a rate constant, k, of 0.05 per year, calculate the expected species diversity after 20 years.