The temperature in a city is modeled by the linear equation T(t)=5t+20*T*(*t*)=5*t*+20, where T(t)*T*(*t*) is the temperature in degrees Celsius and t*t* is the time in hours. What is the rate of change of temperature per hour?

**A)** 5°C per hour

**B)** 20°C per hour

**C)** 25°C per hour

**D)** 50°C per hour

To find the rate of change of temperature per hour, we need to determine the derivative of the temperature equation \( T(t) = 5t + 20 \) with respect to time \( t \).

The derivative of \( T(t) \) with respect to \( t \) is:

\[
\frac{dT}{dt} = 5
\]

This represents the rate of change of temperature per hour.

Thus, the rate of change of temperature is **5°C per hour**.

The correct answer is **A) 5°C per hour**.

Would you like more details or have any questions? Here are some related questions for you:
1. How do derivatives relate to rates of change?
2. What is the physical significance of the slope of a linear equation?
3. Can the rate of change be negative in certain cases?
4. How would you calculate the rate of change for a non-linear equation?
5. What is the unit of measurement for a rate of change?

**Tip:** In many real-world scenarios, the rate of change is represented by the slope of the function.

The temperature in a city is modeled by the linear equation T(t) = 5t + 20, where T(t) is the temperature in degrees Celsius and t is the time in hours. What is the rate of change of temperature per hour?

A) 5°C per hour
B) 20°C per hour
C) 25°C per hour
D) 50°C per hour

Understand how to calculate the rate of change of temperature using the linear equation T(t) = 5t + 20. This problem involves key mathematical concepts like derivatives and rate of change, suitable for Grades 9-10.

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