1. More on Plotting data points.

Every hour the temperature (in Celsius) is recorded starting at midnight and ending at midnight. The Data is the following list:

Hour 0 1 2 3 4 5 6 7 8 9 10 11 12

Temp 6.5 6.1 5.6 4.9 4.2 4.0 4.0 4.8 6.1 8.3 10.0 12.1 14.3

Hour 13 14 15 16 17 18 19 20 21 22 23 24

Temp 16.0 17.3 18.2 18.8 17.6 16.0 14.1 11.5 10.2 9.0 7.9 7.0

(The data is entered below, so you do not need to do any busy-work here).

> data:=[[0,6.5], [1,6.1], [2, 5.6], [3, 4.9], [4, 4.2], [5, 4.0], [6, 4.0], [7, 4.8], [8,6.1], [9,8.3], [10,10.0], [11,12.1], [12,14.3], [13,16.0], [14, 17.3], [15,18.2], [16,18.8], [17,17.6], [18,16.0], [19,14.1], [20,11.5], [21, 10.2], [22,9.0], [23,7.9], [24,7.0]]:

> plot(data, style=point);

Submission:

(a) Find the average rate of change of temperature with respect to time from 6pm to 9pm, from 6pm to 8pm, and from 6pm to 7pm. (Note: 6pm is 18 hours after midnight.)

(b) Explain (in sentences) what these three numbers have to do with slopes in the graph.

(c) Explain why it is not possible to find the instantaneous rate of change of temperature with respect to time at 6pm, but give a reasonable estimate to this instantaneous rate.

Submission worksheet: