Question

 A demographer estimates that the population of inmates at the Nsawam prisons will increase at the rate of 298𝑒0.8𝑥 per year in x years. Currently there are about 7800 inmates at the prison. How many inmates should the prison authorities expect 10 years from now?

Answer 1

$\frac{dN}{dx}=298e^{0.8x}\\ where \space N(x=0) = 7800\\ dN = 298e^{0.8x} dx\\ N=\frac{298e^{0.8x}}{0.8}+C\\ At \space x=0\\ 7800= \frac{298}{0.8}+C \implies C = 7427.5\\ N=\frac{298e^{0.8x}}{0.8}+7427.5\\ N(10)=\frac{298e^{0.8*10}}{0.8}+7427.5\\ N= 1117834.35017\\ N=1117835 \space inmates$