the value, v(m), of a comic - book m months after publication has an average rate of change of - 0.04…

the value, v(m), of a comic - book m months after publication has an average rate of change of - 0.04 between m = 36 and m = 60. which statement must be true?\nthe value of the comic book decreased by a total of $0.04 between m = 36 and m = 60.\nthe value of the comic book increased by a total of $0.04 between m = 36 and m = 60.\nthe value of the comic book decreased by an average of $0.04 each month between m = 36 and m = 60.\nthe value of the comic book increased by an average of $0.04 each month between m = 36 and m = 60.

the value, v(m), of a comic - book m months after publication has an average rate of change of - 0.04 between m = 36 and m = 60. which statement must be true?\nthe value of the comic book decreased by a total of $0.04 between m = 36 and m = 60.\nthe value of the comic book increased by a total of $0.04 between m = 36 and m = 60.\nthe value of the comic book decreased by an average of $0.04 each month between m = 36 and m = 60.\nthe value of the comic book increased by an average of $0.04 each month between m = 36 and m = 60.

Answer

Explanation:

Step1: Recall average rate - of - change definition

The average rate of change of a function $y = f(x)$ over the interval $[x_1,x_2]$ is given by $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. Here, the function is $V(m)$ and the interval is $[36,60]$, and the average rate of change $\frac{V(60)-V(36)}{60 - 36}=- 0.04$.

Step2: Interpret the average rate - of - change

The average rate of change of $-0.04$ means that for each unit increase in $m$ (each month) in the interval $m\in[36,60]$, the value of the function $V(m)$ changes by $-0.04$. A negative average rate of change indicates a decrease. So, on average, the value of the comic - book decreases by $$0.04$ each month between $m = 36$ and $m = 60$.

Answer:

The value of the comic book decreased by an average of $0.04$ each month between $m = 36$ and $m = 60$.