https://file.aiquickdraw.com/mathbot/file/1726629583234a4gfpl5y.jpg

The graph you've uploaded appears to involve a function \( f(t) \) over time \( t \) in hours (x-axis), and the values of \( f(t) \) are in degrees Fahrenheit (y-axis). The two questions are asking for the average rate of change for specific intervals.

### a) Average rate of change from \( f(13) \) to \( f(15) \):
1. The average rate of change between two points \( t = a \) and \( t = b \) is given by:
   \[
   \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
   \]
   For \( t = 13 \) and \( t = 15 \), we need to read the values of \( f(13) \) and \( f(15) \) from the graph.

   From the image, \( f(13) \) seems to be around 70°F, and \( f(15) \) also seems to be around 70°F. So:
   \[
   \frac{f(15) - f(13)}{15 - 13} = \frac{70 - 70}{2} = 0
   \]
   Therefore, the average rate of change from \( f(13) \) to \( f(15) \) is \( 0 \, \text{°F/hour} \).

### b) Average rate of change from \( f(16) \) to \( f(19) \):
1. Again, using the formula for average rate of change, we now focus on \( t = 16 \) and \( t = 19 \).

   From the graph, \( f(16) \) appears to be around 60°F and \( f(19) \) seems to be around 40°F. So:
   \[
   \frac{f(19) - f(16)}{19 - 16} = \frac{40 - 60}{3} = \frac{-20}{3} \approx -6.67 \, \text{°F/hour}
   \]
   Thus, the average rate of change from \( f(16) \) to \( f(19) \) is approximately \( -6.67 \, \text{°F/hour} \).

Would you like any more details or clarifications on these calculations?

### Related Questions:
1. How do you find the instantaneous rate of change at a point on a graph?
2. What is the significance of a zero average rate of change?
3. How does the steepness of a graph's slope relate to the rate of change?
4. How would you interpret a negative average rate of change in a real-world scenario?
5. Can the average rate of change be the same as the instantaneous rate of change?

### Tip:
When calculating the average rate of change, always pay attention to the units, as they help contextualize the meaning of the result (e.g., °F per hour).

What is the average rate of change from f(13) to f(15)? What is the average rate of change from f(16) to f(19)?

Learn how to calculate the average rate of change for the function f(t) from f(13) to f(15) and from f(16) to f(19) using graph interpretation and the average rate of change formula. Suitable for high school students in Grades 9-12.

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