ANSWER and EXPLANATION
a) Yes, the function has a constant rate of change.
Rate of change of a function is the change in y values divided by the change in x values. In other words, the change in the output of the function over the change in the input.
To find the rate of change, we use the formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
We need to pick two points (x1, y1) and (x2, y2).
Let us pick (1,7000) and (3, 1000)
Therefore, the rate of change is:
[tex]\begin{gathered} \frac{1000\text{ - 7000}}{3\text{ - 1}} \\ =\text{ }\frac{-6000}{2} \\ =\text{ -3000 ft/min} \end{gathered}[/tex]
Therefore, the rate of change is -3000 ft/min.
b) The slope of the line is the same as the rate of change, so the slope is -3000 ft/min.
c) The slope and the rate of change are two ways of defining the same concept.
They both tend to measure the change in the output values of a function with respect to the change in the input values.
d) This has the same answer as option C.
