a As dry air moves upward it expands and cools If the ground temperature is 40 C and the temperature at a height of 1 km is 30 C

Question

a As dry air moves upward it expands and cools If the ground temperature is 40 C and the temperature at a height of 1 km is 30 C express the temperature T in C as a function of the height h in kilometers assuming that a linear model is appropriate b Draw the graph of the function in part a What does the slope represent c What is the temperature at a height of 1 5 km SOLUTION a Because we are assuming that T is a linear function of h we can write T mh b We are given that T 40 when h 0 so 40 m b In other words the y intercept is b We are also given that T 30 when h 1 so 30 m The slope of the line is therefore m 30 h TE b The graph is sketched in the figure The slope is m Select with respect to Select c At a height of h 1 5 km the temperature is T 1 5 40 C and the required linear function is C km and this represents the rate of change of

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