Question

1. what is the average rate of change between x=1 and x=6 for the equation: y=1/2(4)^x

Answer 1

Answer:

Step-by-step explanation:

The average rate of change is the slope between the 2 points.  Since this is not a straight line, we are not finding the slope of the function.  If we could use calculus here, we could find the instantaneous rate of change at each of those x coordinates, but we are limited, apparently, so we use what we have!  In order to use the slope formula we have to have 2 coordinates.  So far we have the x coordinates but no corresponding y's.  We will find them by subbing in 1 and 6 for x.  At x = 1:

$y=\frac{1}{2}(4)^1$ so

y = 2 and the resulting coordinate is (1, 2).

At x = 6:

$y=\frac{1}{2}(4)^6$ so

y = 2048 and the resulting coordinate is (6, 2048).

Applying the slope formula:

$m=\frac{2048-2}{6-1}$ and

$m=\frac{2046}{5}$ so

m = 409.2