Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
To determine the correct statement, let's analyze the information given:
1. The value of the comic book, [tex]\( V(m) \)[/tex], has an average rate of change of -0.04 between [tex]\( m = 36 \)[/tex] and [tex]\( m = 60 \)[/tex].
Average rate of change is defined as the change in value divided by the change in time. Here, the average rate of change is [tex]\(-0.04\)[/tex] dollars per month.
2. The time interval is from [tex]\( m = 36 \)[/tex] to [tex]\( m = 60 \)[/tex]. So, the change in time ([tex]\( \Delta m \)[/tex]) is:
[tex]\[ \Delta m = m_{\text{end}} - m_{\text{start}} = 60 - 36 = 24 \text{ months} \][/tex]
3. The total change in value ([tex]\( \Delta V \)[/tex]) over this interval can be calculated using the average rate of change and the change in time:
[tex]\[ \Delta V = \text{rate of change} \times \Delta m = (-0.04) \times 24 = -0.96 \text{ dollars} \][/tex]
Hence, the total change in value of the comic book over this time period is [tex]\(-0.96\)[/tex] dollars, indicating a decrease in value.
Now, examining each statement:
1. "The value of the comic book decreased by a total of [tex]$0.04 between \( m = 36 \) and \( m = 60 \)." - This is incorrect because the total decrease in value is \(-0.96\) dollars, not \(-0.04\) dollars. 2. "The value of the comic book increased by a total of $[/tex]0.04 between [tex]\( m = 36 \)[/tex] and [tex]\( m = 60 \)[/tex]."
- This is incorrect because the comic book's value decreased, not increased.
3. "The value of the comic book decreased by an average of [tex]$0.04 each month between \( m = 36 \) and \( m = 60 \)." - This is correct because the average rate of change is \(-0.04\) dollars per month, indicating a decrease of \(-0.04\) dollars per month on average. 4. "The value of the comic book increased by an average of $[/tex]0.04 each month between [tex]\( m = 36 \)[/tex] and [tex]\( m = 60 \)[/tex]."
- This is incorrect because the rate of change is negative, indicating a decrease, not an increase.
Thus, 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]."
1. The value of the comic book, [tex]\( V(m) \)[/tex], has an average rate of change of -0.04 between [tex]\( m = 36 \)[/tex] and [tex]\( m = 60 \)[/tex].
Average rate of change is defined as the change in value divided by the change in time. Here, the average rate of change is [tex]\(-0.04\)[/tex] dollars per month.
2. The time interval is from [tex]\( m = 36 \)[/tex] to [tex]\( m = 60 \)[/tex]. So, the change in time ([tex]\( \Delta m \)[/tex]) is:
[tex]\[ \Delta m = m_{\text{end}} - m_{\text{start}} = 60 - 36 = 24 \text{ months} \][/tex]
3. The total change in value ([tex]\( \Delta V \)[/tex]) over this interval can be calculated using the average rate of change and the change in time:
[tex]\[ \Delta V = \text{rate of change} \times \Delta m = (-0.04) \times 24 = -0.96 \text{ dollars} \][/tex]
Hence, the total change in value of the comic book over this time period is [tex]\(-0.96\)[/tex] dollars, indicating a decrease in value.
Now, examining each statement:
1. "The value of the comic book decreased by a total of [tex]$0.04 between \( m = 36 \) and \( m = 60 \)." - This is incorrect because the total decrease in value is \(-0.96\) dollars, not \(-0.04\) dollars. 2. "The value of the comic book increased by a total of $[/tex]0.04 between [tex]\( m = 36 \)[/tex] and [tex]\( m = 60 \)[/tex]."
- This is incorrect because the comic book's value decreased, not increased.
3. "The value of the comic book decreased by an average of [tex]$0.04 each month between \( m = 36 \) and \( m = 60 \)." - This is correct because the average rate of change is \(-0.04\) dollars per month, indicating a decrease of \(-0.04\) dollars per month on average. 4. "The value of the comic book increased by an average of $[/tex]0.04 each month between [tex]\( m = 36 \)[/tex] and [tex]\( m = 60 \)[/tex]."
- This is incorrect because the rate of change is negative, indicating a decrease, not an increase.
Thus, 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]."
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.