(Solved): Assume that the US population follows a basic logistic model. The population size is counted in mil ...

Assume that the US population follows a basic logistic model. The population size is counted in millions (of people) and the time is counted in decades. Further assume the following facts: carrying capacity/limit of US population is 4000 mils (or 4 billions). US population in 1990 is 250 mils while US population in 2000 is 275 mils. find the growth rate of the US population and write down the logistic model. plot the slope field. What year should correspond to $t=0$ on the plot? Indicate the equilibrium solution on the plot. sketch some solution curves on the slope field. What does the solution curve looks like if the initial population at $t=0$ is greater than 4000 mils? less than 4000 mils? use separation of variables (S11.4) and partial fraction technique to solve the logistic model. predict the US population in 2100 and 2500.