SOLUTION: Climbing Mount Hood. A group of climbers is planning to climb Mt. Hood in Oregon. They plan to climb the southern route, which starts at Timberline Lodge located approximately 6000

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Question 905499: Climbing Mount Hood. A group of climbers is planning to climb Mt. Hood in Oregon. They plan to climb the southern route, which starts at Timberline Lodge located approximately 6000 feet above sea level. The altitude at the summit of Mt feet. hood is approximately 11240 feet. Air temperature drops approximately 0.21°F for every 100 feet you rise in altitude.
a. If the temperature at Timberline Lodge is 34°F, what is the temperature on the mountain 500 feet above Timberline? 1500 feet above Timberline.
b. If the temperature at Timberline is 34°F, write an equation for the temperature in terms of the number of feet above the lodge.
c. Draw a graph for this problem. Consider what values would be reasonable to include for each of the axes.
d. If the temperature at Timberline Lodge is 34°F is there a point on the mountain where the temperature drops to freezing? If yes, what is the height above sea level where this occurs?
e. If the temperature at Timberline Lodge is 34°F, what is the temperature at the summit?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
They plan to climb the southern route, which starts at Timberline Lodge located approximately 6000 feet above sea level.
The altitude at the summit of Mt feet. hood is approximately 11240 feet.
Air temperature drops approximately 0.21°F for every 100 feet you rise in altitude
;
a. If the temperature at Timberline Lodge is 34°F, what is the temperature on the mountain 500 feet above Timberline?
34 - 5(.21) = 32.95
At 1500 ft
34 - 15(.21) = 30.85
;
b. If the temperature at Timberline is 34°F, write an equation for the temperature in terms of the number of feet above the lodge.
x = ft above the lodge
f(x) = -%28.21x%29%2F100 + 34
:
c. Draw a graph for this problem. Consider what values would be reasonable to include for each of the axes.
x:-1000 to +6000; y:-10 to + 40
+graph%28+300%2C+200%2C+-1000%2C+6000%2C+-10%2C+40%2C+%28-%28.21x%29%2F100%29%2B34%2C+32%29+
:
d. If the temperature at Timberline Lodge is 34°F is there a point on the mountain where the temperature drops to freezing? If yes, what is the height above sea level where this occurs?
+graph%28+300%2C+200%2C+-100%2C+1100%2C+-10%2C+40%2C+%28-%28.21x%29%2F100%29%2B34%2C+32%29+
On the graph looks like at 950 ft above the lodge
or you can solve for x for a more exact answer
-%28.21x%29%2F100 + 34 = 32
:
e. If the temperature at Timberline Lodge is 34°F, what is the temperature at the summit?
f(x) = 11240-6000 = 5240
f(x) = -%28.21%285240%29%29%2F100 + 34
f(x) = 23 degrees