Find equations for exponential functions that pass through the pairs of points given...

Find equations for exponential functions that pass through the pairs of points given Exercise. (Round all coefficients to 4 decimal places when necessary.) HINT [See Example 2.]

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

Through (2, −4) and (4, −16)