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. What is the average rate of change of temperature (in °F/ft)?
How much does the temperature change (in degrees F) when the altitude increases by 100 feet?
The temperature decreases by ? °F for every 100 feet up the mountain.
show your work
To find the average rate of change of temperature in °F/ft, we need to calculate the difference in temperature and altitude and then divide them.
Temperature change = 68°F - 54°F = 14°F
Altitude change = 2000 ft - 0 ft = 2000 ft
Average rate of change = Temperature change / Altitude change
Average rate of change = 14°F / 2000 ft = 0.007°F/ft
Now, to find how much the temperature changes in degrees Fahrenheit when the altitude increases by 100 feet, we can use the calculated average rate of change.
Temperature change for 100 ft = Average rate of change * Altitude change
Temperature change for 100 ft = 0.007°F/ft * 100 ft = 0.7°F
Therefore, the temperature decreases by 0.7°F for every 100 feet up the mountain.