Freon Production The production of ozone-layer damaging Freon 22 (chlorodi...

Freon Production The production of ozone-layer damaging Freon 22 (chlorodifluoromethane) in developing countries rose from 200 tons in 2004 to a projected 590 tons in 2010.

a. Use this information to find both a linear model and an exponential model for the amount F of Freon 22 (in tons) as a function of time t in years since 2000. (Round all coefficients to three significant digits.) HINT [See Example 2.] Which of these models would you judge to be more appropriate to the data shown below:

b. Use the better of the two models from part (a) to predict the 2008 figure and compare it with the projected figure above.

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