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The question is asking about a periodic function based on the given values in the table and seeks to find the period, amplitude, and some function values at specific times.

Let's break it down:

1. **Periodicity:**
   - The function values appear to repeat over a specific interval, which suggests periodic behavior. Looking at the values of \( t = 20 \) to \( t = 60 \), we see that the function follows a pattern. The problem specifies that the function repeats itself after 25 units (the difference between 20 and 45), so the period is **25**.

2. **Amplitude:**
   - Amplitude is the difference between the maximum value and the average or midline value of the function. The max value from the table is 2.3, and the min value is 1.4. The amplitude is calculated as:
   \[
   \text{Amplitude} = \frac{\text{Max} - \text{Min}}{2} = \frac{2.3 - 1.4}{2} = 0.45
   \]
   So, the amplitude is **0.45**.

3. **Function values at specific points:**
   - \( f(15) \): Since the period is 25, \( f(15) \) can be found by considering the nearest corresponding value in the periodic table. \( t = 15 \) is close to \( t = 20 \), and \( f(20) = 1.8 \), so \( f(15) = 1.8 \).
   - \( f(70) \): Since the period is 25, we can subtract the period from 70 to find the equivalent time within the period. \( 70 - 25 = 45 \), and \( f(45) = 2.0 \), so \( f(70) = 2.0 \).
   - \( f(130) \): Similarly, subtracting multiples of the period from 130 gives us \( 130 - 100 = 30 \), and \( f(30) = 1.4 \), so \( f(130) = 1.4 \).

Thus, the correct values to enter are:

- The period: **25**
- The amplitude: **0.45**
- \( f(15) = 1.8 \)
- \( f(70) = 2.0 \)
- \( f(130) = 1.4 \)

Would you like a more detailed explanation on how periodicity or amplitude works?

Here are 5 related questions for deeper understanding:
1. What is the general formula for a sinusoidal periodic function?
2. How would the function behave if the period was doubled?
3. How do you determine the phase shift in a periodic function?
4. Can a periodic function have different amplitudes over time?
5. How does the concept of frequency relate to the period of a function?

**Tip:** For any periodic function, the period is the smallest interval over which the function repeats itself.

Values of a function are given in the following table. Explain why this function appears to be periodic. Approximately what are the period and amplitude of the function? Assuming that the function is periodic, estimate its value at t = 15, t = 70, and t = 130.

Explore how to determine the period and amplitude of a periodic function based on table data. This problem explains periodicity, amplitude, and how to estimate function values at specific points, suitable for Grades 9-12.

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