Question

The image shows the graph of T , the temperature (in Fahrenheit) over a 20-hour period in Peach

Tree City as a function of time T




1. Estimate T(10)
2. If t=0 corresponds to 12:00 midnight, interpret what is meant by T(12) in words
3. Estimate the highest temperature during this period from the graph.
4. When was the temperature decreasing?
5. If Taylor Swift wants to go for a two-hour hike and return before the temperature gets
over 70 degrees, when should she leave?

Answer 1

1. T(10) = 80

2. if t = 0 is 12am, then t = 12 is 12pm, as 12 hours would have passed since then. T(t) is the change in temperature, so when t = 12, T(12) ≈ 85. So when it was 12pm, the temperature was 85°F.

3. The maxima of the graph is at t = 16, T(16) = 90 degrees is the highest temperature during this period.

4. Temperature was decreasing during the time interval (16, 20), that is 4pm to 8pm

5. When t < 6 is when T(t) < 70. Therefore, she may leave at t = 0 or 12am.

Explanation:

Answer 2

The given graph shows the relation between Temperature (T) and time (t).

1. Estimate T(10).

The expression T(10) refers to the vertical coordinate assigned to x = 10, which is shown in the graph. There you can observe that x = 10 is assigned to y = 80.

Therefore, T(10) = 80

2. If t = 0 corresponds to 12:00 midnight, interpret what is meant by T(12) in words.

We know that the independent variable (horizontal axis) represents time, which means that T(12) refers to the temperatura after 12 hours. If t = 0 is midnight, then T(12) is the temperature at 12:00 midday.

3. Estimate the highest temperature during this period from the graph.

According to the given graph, the higher temperature shown is 90 °F. Remember that vertical axis represents Temperature.

4. When was the temperature decreasing?

In the graph we observe that the temperature begin to decreasing after 16 hours, that is, 4pm.

5. If Taylor Swift wants to go for a two-hour hike and return before the temperature gets over 70 degrees, when should she leave?

She should leave at hour six, because at that moment the temperature is already 70 degrees, if she stay a little more, she will feel temperatures over 70 degrees.