U.S. Population The U.S. population was 180 million in 1960 and 303 millio...

U.S. Population The U.S. population was 180 million in 1960 and 303 million in 2008.

a. Use these data to give an exponential growth model showing the U.S. population P as a function of time t in years since 1960. Round coefficients to 6 significant digits. HINT [See Example 2.]

b. By experimenting, determine the smallest number of significant digits to which you should round the coefficients in part (a) in order to obtain the correct 2008 population figure accurate to three significant digits.

c. Using the model in part (a), predict the population in 2020.

Example 2:

Find an equation of the exponential curve through (1, 6.3) and (4, 170.1).

Solution We want an equation of the form

Substituting the coordinates of the given points, we get

If we now divide the second equation by the first, we get

Now that we have b, we can substitute its value into the first equation to obtain

We have both constants, A = 2.1 and b = 3, so the model is