World Population World population was estimated at 2.56 billion people in...

World Population World population was estimated at 2.56 billion people in 1950 and 6.72 billion people in 2008.

a. Use these data to give an exponential growth model showing the world population P as a function of time t in years since 1950. 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 to three significant digits.

c. Assuming the exponential growth model from part (a), estimate the world population in the year 1000. Comment on your answer.

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