For the following problems, set up and solve the differential equations.

The human population (in thousands) of Nevada in 1950 was roughly 160 . If the carrying capacity is

estimated at 10 million individuals, and assuming a growth rate of 2$\%$ per year, develop a logistic growth model and solve for the population in Nevada at any time (use 1950 as time $=0$ ). What population does your model predict for 2000 ? How close is your prediction to the true value of $1,998,257 ?$