Satellite Radio Subscriptions The number of Sirius Satellite Radio subscri...

Satellite Radio Subscriptions The number of Sirius Satellite Radio subscribers grew from 0.3 million in 2003 to 3.2 million in 2005.

a. Use this information to find both a linear model and an exponential model for the number N of subscribers (in millions) 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 2006 figure. (The actual 2006 figure was approximately 6 million subscribers.)

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