Chapter 1.4, Problem 5E

5. United States Population Growth In 1960 the population of the United States was about 180 million. Since that time, the population has increased by approximately 1.2% each year. This is a verbal description of the function $N=N\left(t\right)$, where $N$ is the population, in millions, and $t$ is the number of years since 1960.

a. Express in functional notation the population of the United States in 1963. Calculate its value.

b. Use the verbal description of N to make a table of values that shows U.S. population in millions from 1960 through 1965.

c. Make a graph of U.S. population versus time. Be sure to label your graph appropriately.

d. Verify that the formula $180\times {1.012}^t\text{million}$ people, where $t$ is the number of years since 1960, gives the same values as those you found in the table in part b. (Note: Because $t$ is the number of years since 1960, you would use t = 2 to get the population in 1962.)

e. Assuming that the population has been growing at the same percentage rate since 1960, what value does the formula above give for the population in 2000? (Note: The actual population in 2000 was about 281 million.).