Chapter 1.8, Problem 68ES

The population $p$ of the United States (in millions) in year $t$ can be modelled by the function $p\left(t\right)=\frac{525}{1+1.1e^{-0.02225\left(t-1990\right)}}$

(a) Based on this model, what was the U.S. population in $1990$ ?

(b) Plot $p$ versus $t$ for the $200$ -year period from $1950$ to $2150$ .

(c) By evaluating an appropriate limit, show that the graph of $p$ versus $t$ has a horizontal asymptote $p=c$ for an appropriate constant $c$ .

(d) What is the significance of the constant c in part (c) for the population predicted by this model?