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The rate of increase in the number of hours of daylight (in hr/day) is:

- On April 21 (t = 111): \( L'(t) = 0.0415 \, \text{hr/day} \)
- On May 21 (t = 141): \( L'(t) = 0.0240 \, \text{hr/day} \)

Would you like more details on the calculation process or have any questions?

Here are 5 related questions to expand on the topic:
1. What does the function \( L(t) \) model about daylight?
2. How would the rate of change differ as you approach the summer solstice?
3. Can you interpret what a higher or lower derivative value means physically in terms of daylight hours?
4. How would you calculate the maximum daylight hours using this model?
5. How does the length of daylight change as the seasons transition?

**Tip:** The derivative of a function gives the rate of change, which can help in understanding trends like increasing or decreasing daylight throughout the year.

A model for the length of daylight (in hours) in Philadelphia on the t-th day of a particular year is L(t) = 12 + 2.8 sin[(2π/365)(t - 80)]. Use this model to compare how the number of hours of daylight is increasing (in hr/day) in Philadelphia on April 21 (t = 111) and May 21 (t = 141).

Explore how to calculate the rate of change in the number of daylight hours in Philadelphia using the model L(t) = 12 + 2.8 sin[(2π/365)(t - 80)]. Learn how to find the derivatives to compare the daylight increase on April 21 and May 21.

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