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.