Chapter 4.6, Problem 39PE

(a)

To determine

To calculate: Evaluate $P(0)$ and interpret its meaning in context for $P(t)=\frac{725}{1+8.295e^{-0.0165t}}$.

(b)

To determine

To calculate: Predict U.S. population on January $1,2020$ if $P(t)=\frac{725}{1+8.295e^{-0.0165t}}$

(c)

To determine

To calculate: Predict U.S. population on January $1,2050$, if $P(t)=\frac{725}{1+8.295e^{-0.0165t}}$

(d)

To determine

To calculate: The year during which U.S. population will reach $500$ million.

(e)

To determine

To calculate: What value will the term $\frac{8.295}{e^{0.0165t}}$ approaches as $t\to \infty$?

(f)

To determine

To calculate: The limiting value of $P(t)$, if $P(t)=\frac{725}{1+8.295e^{-0.0165t}}$