On a hike, Parker noticed that the temperature at the base of a mountain was 68°F. At a point on the mountain that was 2,000 feet above the base, the temperature was 54°F.
A) What is the average rate of change of temperature (in °F/ft)?
My answer: -0.007 °F/ft
B) How much does the temperature change (in degrees F) when the altitude increases by 100 feet?
My Answer: The temperature decreases by .07 °F for every 100 feet up the mountain.
A) To find the average rate of change of temperature, we use the formula:
Average rate of change = (change in temperature) / (change in altitude)
Change in temperature = 54°F - 68°F = -14°F
Change in altitude = 2000 ft - 0 ft = 2000 ft
Average rate of change = -14°F / 2000 ft = -0.007°F/ft
Therefore, the average rate of change of temperature is -0.007°F/ft.
B) To find how much the temperature changes when the altitude increases by 100 feet, we can use the average rate of change we found in part A.
Change in temperature = average rate of change x change in altitude
Change in temperature = -0.007°F/ft x 100 ft = -0.7°F
Therefore, the temperature decreases by 0.7°F for every 100 feet up the mountain.