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To find \( a(2.6) \), we first need to understand the function \( a(t) = f(t) + 5 \).

This means that \( a(t) \) is simply the value of \( f(t) \) shifted upwards by 5 units.

### Steps:
1. **Find \( f(2.6) \):**
   - From the graph, we need to determine the value of \( f(t) \) at \( t = 2.6 \).
   
   Observing the graph:
   - Around \( t = 2.6 \), the graph is sloping upward and seems to be between \( f(2) = 3 \) and \( f(3) = 3 \). From the trend, \( f(2.6) \) appears to be close to 5.
   
2. **Apply the transformation for \( a(t) \):**
   - Since \( a(t) = f(t) + 5 \), we have:
   \[
   a(2.6) = f(2.6) + 5 = 5 + 5 = 10.
   \]

Thus, \( a(2.6) = 10 \).

Would you like more details or have any questions?

### Related Questions:
1. What is \( b(2.6) = f(2.6 + 12) \)?
2. What is \( c(2.6) = f(2.6 - 12) - 3 \)?
3. How would the graph change for \( f(t) + 5 \)?
4. What is the significance of shifting a function vertically?
5. How do we interpret horizontal shifts in the graph?

### Tip:
When shifting a graph vertically, you simply add or subtract the shift value from the y-coordinates of every point on the graph without changing the x-coordinates.

This problem involves finding the value of a(2.6) for the function a(t) = f(t) + 5. Learn how to interpret the graph of f(t) and apply transformations such as vertical shifts. Suitable for Grades 10-12.

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