Chapter 4.2, Problem 55PE

(a)

To determine

Whether the graph of $P\left(t\right)=310{\left(1.0097\right)}^t$ is an increasing or decreasing exponential function where t is time in years since 2010. When approximate initial population is 310 million with 0.97% annual growth rate.

(b)

To determine

To calculate: The value of $P\left(0\right)$ and interpret its meaning for population function $P\left(t\right)=310{\left(1.0097\right)}^t$, where t is time in years since 2010 when approximate initial population is 310 million with 0.97% annual growth rate.

(c)

To determine

To calculate: The value of $P\left(10\right)$ and interpret its meaning for population function $P\left(t\right)=310{\left(1.0097\right)}^t$ when approximate initial population is 310 million with 0.97% annual growth rate.

(d)

To determine

To calculate: The values of $P\left(20\right)$, $P\left(30\right)$, and interpret its meaning for population function $P\left(t\right)=310{\left(1.0097\right)}^t$ when approximate initial population is 310 million with 0.97% annual growth rate.

(e)

To determine

To calculate: The values of $P\left(200\right)$ and interpret its meaning for population function $P\left(t\right)=310{\left(1.0097\right)}^t$, where t in years since 2010, when approximate initial population is 310 million with 0.97% annual growth rate. Also, determine whether this model can be continue indefinitely.