2. Temperature and Illumination
Alone in your dim, unheated room, you light a single candlerather than curse the darkness. Depressed with the situation, youwalk directly away from the candle, sighing. The temperature (indegrees Fahrenheit) and illumination (in % of one candle power)decrease as your distance (in feet) from the candle increases. Infact, you have tables showing this information. (tables are in thetext).
You are cold when the temperature is below 40â—¦. You are in thedark when the illumination is at most 50% of one candle power.
(a)TwographsareshowninFigures2.70and2.71.Oneistemperatureasafunctionofdistanceand one is illumination as a function of distance. Which is which?Explain.
Figure 2.70 Figure 2.71
(b) What is the average rate at which the temperature ischanging when the illumination drops from 75% to 56%?
(c) You can still read your watch when the illumination is about65%. Can you still read your watch at 3.5 feet? Explain.
(d) Suppose you know that at 6 feet the instantaneous rate ofchange of the temperature is −4.5◦F/ft and the instantaneous rateof change of illumination is −3% candle power/ft. Estimate thetemperature and the illumination at 7 feet.
(e) Are you in the dark before you are cold, or vice versa?
