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Bài 2.Một nhà nghiên cứu ước tính rằng sau t giờ từ lúc nửa đêm trong khoảng thời gian 24 giờ, nhiệt độ ở phía Bắc của một thành phố ABC được cho bởi 
đô C.

Tính nhiệt độ trung bình trong thành phố ABC từ 5 giờ sáng đến 4 giờ chiều.

The function provided for the temperature \( C(t) \) is:

\[
C(t) = 6 - \frac{2}{5}(t - 14)^2
\]

with the time \( t \) ranging from 0 to 24 hours. You are asked to find the average temperature in the city ABC between 5:00 AM (which corresponds to \( t = 5 \)) and 4:00 PM (which corresponds to \( t = 16 \)).

To compute the average temperature over the interval \( t \in [5, 16] \), we will use the following formula for the average value of a continuous function \( C(t) \) over an interval \([a, b]\):

\[
\text{Average temperature} = \frac{1}{b-a} \int_{a}^{b} C(t) \, dt
\]

Here, \( a = 5 \), \( b = 16 \), and \( C(t) = 6 - \frac{2}{5}(t - 14)^2 \).

Let me calculate the integral of this function over the interval \( [5, 16] \).The average temperature in the city ABC from 5:00 AM to 4:00 PM, based on the given model, is approximately \(-2.93^\circ C\). This suggests that the temperature is quite cold during this period, with an average below freezing.

Would you like more details or have any questions?

Here are some related questions you might want to explore:
1. What is the maximum temperature during the 24-hour period?
2. At what time of the day does the temperature reach its lowest point?
3. How does the temperature change during different times of the day?
4. What is the integral of the temperature function over the entire 24-hour period?
5. Can we find the temperature at specific hours like 6 AM, 12 PM, and 8 PM?

**Tip**: Integrating a function over time gives us valuable insights about trends like averages and total changes within specific intervals.

Tính nhiệt độ trung bình trong thành phố ABC từ 5 giờ sáng đến 4 giờ chiều.

Learn how to calculate the average temperature in city ABC from 5:00 AM to 4:00 PM using the function C(t) = 6 - (2/5) * (t - 14)^2. This problem involves calculus concepts such as the definite integral and the average value of a function.

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