Question

Find the average rate of change from x = 3 to x = 15 for the function f(x) = 0.01(2)x

Answer 1

The average rate of change for this is the slope of the secant line that connects those 2 points (3, y) and (15, y).  What we need for the slope formula of change in y over change in x are the y values which are unknown as of right now. We can find them though! Don't worry! The equation is y = .01(2)^x. Using that equation, let's sub in both the 3 and the 15 and find the corresponding y values. Subbing in first a 3 gives you y = .01(2)^3, and y = .08.  Subbing in a 15 gives you y = .01(2)^15 and y = 327.68. Now we have the coordinates we need to find the slope of the secant line connecting those 2 points: (3, .08) and (15, 327.6). Fitting those into the slope formula gives us (327.68-.08)/(15-3). Simplifying that is 327.6/12 which divides out to 27.3