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The provided table shows that the function \( f(t) \) starts repeating values, which suggests that it is periodic. Here's the breakdown to answer the questions:

### 1. **Period**
- The values repeat after \( t = 60 \). Looking at the values at \( t = 20, 25, 30, \dots \), we see that \( f(20) = 1.8 \), \( f(25) = 1.4 \), \( f(30) = 1.7 \), and this pattern repeats again at \( t = 60 \).
- Therefore, the period is:
  \[
  T = 60 - 20 = 40.
  \]

### 2. **Amplitude**
- The amplitude of a periodic function is given by:
  \[
  A = \frac{\text{max value} - \text{min value}}{2}.
  \]
- From the table, the maximum value is 2.3, and the minimum value is 1.4.
  \[
  A = \frac{2.3 - 1.4}{2} = 0.45.
  \]

### 3. **Function Values at Specific \( t \):**
- The function is periodic with a period of 40, so to find \( f(15) \), \( f(70) \), and \( f(130) \), we can reduce these values mod 40:

  - \( t = 15 \equiv t = 55 \pmod{40} \), so \( f(15) = f(55) = 1.7 \).
  - \( t = 70 \equiv t = 30 \pmod{40} \), so \( f(70) = f(30) = 1.7 \).
  - \( t = 130 \equiv t = 50 \pmod{40} \), so \( f(130) = f(50) = 1.8 \).

### Final Answers:
- The period is 40.
- The amplitude is 0.45.
- \( f(15) = 1.7 \).
- \( f(70) = 1.7 \).
- \( f(130) = 1.8 \).

Would you like any further clarifications or additional details?

Here are 5 related questions to deepen your understanding:
1. How can you determine the period of a function if only part of the graph is available?
2. What is the physical interpretation of amplitude in real-world periodic functions?
3. How can you find the phase shift in a periodic function?
4. Why is the modulus operation useful in finding values of periodic functions?
5. How would you determine the frequency from the period?

**Tip**: When identifying periodicity, always look for 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, at t = 70, and at t = 130.

Learn how to determine the period and amplitude of a periodic function using a given table of values. This problem includes finding the period as the interval over which the function repeats and calculating the amplitude from the maximum and minimum values. Suitable for students in Grades 9-12.

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