Certainly! Let's break down the problem and arrive at the correct statement:
1. Understanding the Given Information:
- The value [tex]\( V(m) \)[/tex] of the comic book has an average rate of change of [tex]\(-0.04\)[/tex] between [tex]\( m = 36 \)[/tex] and [tex]\( m = 60 \)[/tex].
- We interpret this as the comic book's value decreases by [tex]\(\$0.04\)[/tex] on average each month between the 36th and 60th months.
2. Determine the Time Period:
- The time period under consideration is from month 36 to month 60.
3. Calculating the Duration:
- The duration of the time period is:
[tex]\[
60 - 36 = 24 \text{ months}
\][/tex]
4. Calculating the Total Change in Value:
- Given the average rate of change is [tex]\(-0.04\)[/tex] dollars per month, over 24 months, the total change in value is determined as:
[tex]\[
-0.04 \times 24 = -0.96
\][/tex]
- The negative sign indicates a decrease in value.
In summary:
- The value of the comic book decreased by [tex]\(\$ 0.04\)[/tex] each month on average between the 36th and 60th months.
- The total decrease in value over these 24 months is [tex]\(\$ 0.96\)[/tex].
Given the choices, the correct statement is:
- The value of the comic book decreased by an average of \$ 0.04 each month between [tex]\( m=36 \)[/tex] and [tex]\( m=60 \)[/tex].
