The question asks to find the rate of the total change in temperature over time, given two temperature changes:

• The temperature increased by 16°F in 5 hours.
• The temperature decreased by 31°F in the next 8 hours.

Step-by-Step Solution:

1. Calculate the total change in temperature:

   • The increase in temperature is +16°F.
   • The decrease in temperature is -31°F.
   • The total change in temperature is $16°F - 31°F = -15°F$.

2. Calculate the total time:

   • The first period is 5 hours.
   • The second period is 8 hours.
   • The total time is $5 + 8 = 13$ hours.

3. Find the rate of change:

   • The rate of change is the total change in temperature divided by the total time. $\text{Rate of change} = \frac{-15°F}{13 \text{ hours}}.$

So, the correct expression that shows the rate of the total change in temperature is A. $\frac{-15°F}{13 \text{ hours}}$.

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Related Questions:

1. What is the formula to calculate rate of change in general?
2. How do you interpret a negative rate of change?
3. What would the rate of change be if the temperature only decreased by 10°F in the same time period?
4. Can the rate of change be 0? Under what conditions?
5. How would this problem change if the temperature first decreased and then increased?

Tip: Always remember that a negative rate of change means a decrease over time!