Question

during a certain time of year, the daily temperature in a certain city, in degrees celsius follows a periodic pattern. the graph below shows the temperature over two days, where time t is measured in hours after 12:00 a.m. (midnight) on the first day. what is the amplitude and what does it represent in this context?

Explanation:

Step1: Identify maximum and minimum values

The maximum temperature is 23 degrees Celsius (at \(t = 14.5\) and \(t=38.5\)) and the minimum temperature is 9 degrees Celsius (at \(t = 2.5\) and \(t = 26.5\)).

Step2: Calculate the amplitude

The formula for the amplitude \(A\) of a periodic - function is \(A=\frac{\text{Max}-\text{Min}}{2}\). Substituting \(\text{Max}=23\) and \(\text{Min}=9\) into the formula, we get \(A=\frac{23 - 9}{2}\).
\[A=\frac{14}{2}=7\]

Step3: Interpret the amplitude

In the context of daily temperature, the amplitude represents half of the difference between the maximum and minimum daily temperatures. It shows the amount by which the temperature varies above and below the average (mid - line) temperature over the course of a day.

Answer:

The amplitude is 7 degrees Celsius. It represents half of the difference between the maximum and minimum daily temperatures in the city.