Ma 141 Problem Set 5 Name Date 1 . Suppose the length, L cm, of a steel bar depends on the air temperature, TC, which itself depends on time t, measured in hours. If the length increases by 1.5 cm for every degree increase in temperature and the temperature is increasing at 2'C per hour, how fast is the length of the bar increasing? Hint: let L = f(1) and T = g(t); find the value of T by using the Chain Rule. 2. Ecologists estimate that, when the population of a certain city is x thousand persons, the average level L of carbon monoxide in the air above the city will be L ppm (parts per million), where L = 10 + 0.4x + .0001x2. The population of the city is estimated to be x = 752 + 23t + 0.5t thousand persons t years from the present. a. Find the function that describes the rate of change of carbon monoxide with respect to the population of the city. b. How fast is the population changing when t = 2? C. How fast (with respect to time) is the carbon monoxide level changing at time t = 2? Hint: by the chain rule, dL - dL dx dt dx dt