Let P $=$ f$($t$)$ represent the US population in millions in year t$.$

$($a$)$ What does the statement f$(2005)=296$ tell you about the US population?

In $296$ years there will be $2005$ million people in the US$.$The US population was $296$ million people in $2005.296$ million people were born in the US in $2005.$There were at most $296$ million people in the US before the year $2005.$

$($b$)$ f $1(296)=--$Units$--$ millions of people millions of people per year years years per million people

Interpret f $1(296).$

This was the number of people in the US in the year $296.$This was the year in which the US population was $296$ million.$$This was the US population in the year $296.$This was how fast the US population grew by the year $2005.$

$($c$)$ What does the statement f $\text{'}(2005)=2\mathrm{.}65$ tell you about the population?

The range of the US population in $2005$ was about $2\mathrm{.}65$ million people.The US population grew by about $2\mathrm{.}65$ million people between $2005$ and $2006.$The US population was constant for $2\mathrm{.}65$ years before $2005.$The US population grew by $2005$ million people over $2\mathrm{.}65$ years.

What are the units of f $\text{'}(2005)?$

yearsmillions of people per year$$years per million peoplemillions of people

$($d$)($f $1)\text{'}(296)=--$Units$--$ years millions of people per year millions of people years per million people

Interpret $($f $1)\text{'}(296).$

The US population reached $296$ million people this many years after the year $2000.$This was the number of years it took the US population to increase by one million people when the population was $296$ million.$$This was how long the US population stayed at $296$ million people.This was the rate at which the US population grew when the population was $296$ million people.