Alone in your dim, unheated room, you light a single candle rather than curse the darkness. Depressed with the situation, you walk directly away from the candle, sighing. The temperature (in degrees Fahrenheit) and illumination (in % of one candle power) decrease as your distance (in feet) from the candle increases. In fact, you have tables showing this information.

You are cold when the temperature is below 40◦. You are in the dark when the illumination is at most 50% of one candle power.
(a) Two graphs are shown in Figures 2.67 and 2.68. One is temperature as a function of distance and one is illumination as a function of distance. Which is which? Explain.

(b) What is the average rate at which the temperature is changing when the illumination drops from 75% to 56%?
(c) You can still read your watch when the illumination is about 65%. Can you still read your watch at 3.5 feet? Explain.
(d) Suppose you know that at 6 feet the instantaneous rate of change of the temperature is −4.5^◦F/ft and the instantaneous rate of change of illumination is −3% candle power/ft. Estimate the temperature and the illumination at 7 feet.
(e) Are you in the dark before you are cold, or vice versa?

Distance (feet) 0 1 2 3 4 5 6 6 Temperature (F) 55 54.5 53.5 52 50 47 43.5 Distance (feet) 0 1 2 3 4 5 6 Illumination (%) 100 85 75 67 60 56 53