Answer:
Step-by-step explanation:
To find the average rate of change in temperature between 9 am and 5 pm, we need to determine the change in temperature divided by the change in time.
Let's denote the temperature at 9 am as \( T_1 \) (in Celsius) and the temperature at 5 pm as \( T_2 \) (in Celsius). Also, let's denote the time at 9 am as \( t_1 \) (in hours) and the time at 5 pm as \( t_2 \) (in hours).
The average rate of change in temperature, \( \text{Avg. Rate} \), is given by the formula:
\[ \text{Avg. Rate} = \frac{T_2 - T_1}{t_2 - t_1} \]
First, we need to determine the temperatures and times from the graph. Let's say \( T_1 = 15^\circ \text{C} \) (at 9 am) and \( T_2 = 30^\circ \text{C} \) (at 5 pm). The corresponding times are \( t_1 = 9 \) am and \( t_2 = 5 \) pm, which is 8 hours later.
Now, plug in the values into the formula:
\[ \text{Avg. Rate} = \frac{30^\circ \text{C} - 15^\circ \text{C}}{5 \text{ hours} - 9 \text{ hours}} \]
Simplifying:
\[ \text{Avg. Rate} = \frac{15^\circ \text{C}}{-4 \text{ hours}} \]
Dividing the numerator and denominator by their greatest common divisor, which is 1:
\[ \text{Avg. Rate} = \frac{-15^\circ \text{C}}{4 \text{ hours}} \]
Therefore, the average rate of change in temperature between 9 am and 5 pm is \( -\frac{15}{4} \) degrees Celsius per hour, which can also be written as \( -3.75^\circ \text{C/hr} \).
