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

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:

so

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

At x = 6:

so

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

Applying the slope formula:

and

so

m = 409.2

answer: 25.4 units

step-by-step explanation: radius = 12.7 units

diameter = twice the radius

diameter = 12.7 x 2

= 25.4