Final Answer:
The equation that represents the value V of the popular comic book after t years is V = t² + 2t + 1. Option C is answer.
Step-by-step explanation:
Key Considerations:
Initial Value: The value of the comic book should be positive at the initial time (t = 0). This eliminates options b and d, as they both result in a value of 1 at t = 0.
Increasing Value: The value of the comic book is expected to increase over time, as it's likely to become more valuable as it ages. This further narrows our choices to option c, as it's the only remaining equation that produces an increasing value for t > 0.
Breakdown of Option c (V = t² + 2t + 1):
Positive Quadratic Term: The term t² ensures that the value grows as t increases, indicating a positive overall trend.
Positive Linear Term: The term 2t contributes to the overall increase in value, further supporting the expected growth pattern.
Positive Constant Term: The term 1 represents the initial value of the comic book, ensuring a positive starting point.
Conclusion:
Based on these considerations, the equation V = t² + 2t + 1 accurately reflects the expected behavior of the comic book's value over time, making it the most suitable representation among the given choices.
Option C is answer.