Question

The value, V(m), of a comic book m months after publication has a average rate of change of -0.04 between m = 36 and m = 60. Which statement must be true?
A.) The value of the comic book decreased by a total of $0.04 between m = 36 and m = 60.
B.) The value of the comic book increased by a total of $0.04 between m = 36 and m = 60.
C.) The value of the comic book decreased by an average of $0.04 each month between m = 36 and m = 60.
D.) The value of the comic book increased by an average of $0.04 each month between m = 36 and m = 60.

Answer 1

So average rate of change from m=a to m=b can be found from the following formula:
\[\frac{f(b)-f(a)}{b-a}\]

Answer 2

you can replace f with V

Answer 3

Didn't see the choices just a sec ago.

Answer 4

But anyways the key word is average and you should also notice the sign that is in front of this average.

Answer 5

IF \[\frac{V(b)-V(a)}{b-a}=\text{ negative number }\]
then don't you think the average would be decreasing?

Answer 6

and if we had \[\frac{V(b)-V(a)}{b-a}=\text{ positive number } \]
then wouldn't the average be increasing?

Answer 7

Think about the slope of lines.
Because the average rate of change is using a secant line. IF the slope of the line is positive, then the line is increasing. If the slope of the line is negative, then the line is decreasing.