SOLUTION: Help, I am trying to help my daughter with her homework, don't know what I'm doing. Hope you can help. Calorie consumption problem: Lansburg's Weather and Health reports data

Question 109443: Help, I am trying to help my daughter with her homework, don't know what I'm doing. Hope you can help.
Calorie consumption problem: Lansburg's Weather and Health reports data gathered during World War II which shows that people use about 35 more calories per day for each 1 degree drop in the Celsius temp. At 20 degrees C, a working person uses about 2900 calories per day.
a) Explain how you know that the calorie consumption varies linerarly with the temp. What is the slope? write the equation.
b) How many calories per day would a working person use:
in the Sahara Desert wht eht temp is 50 C.
in Antarctica in August when the temp is -50 C.
c) At what temp does your model predict that a working person would use no calories at all.
d) Do you think the linear function gives meaningful answers for temp this hot?
e) Sketch a graph of the function using a reasonable domain.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Calorie consumption problem: Lansburg's Weather and Health reports data gathered during World War II which shows that people use about 35 more calories per day for each 1 degree drop in the Celsius temp. At 20 degrees C, a working person uses about 2900 calories per day.
a) Explain how you know that the calorie consumption varies linerarly with the temp. What is the slope? write the equation.
Why linear?: The use of calories per day changes at a CONSTANT RATE of
+35 for every -1 change in Celsius temperature.
------
Slope = -35 because as temperature INCREASES one degree calorie use decreases
by 35.
------------

b) How many calories per day would a working person use:
in the Sahara Desert when the temp is 50 C.
EQUATION:
Remember 2900 calories are needed when temp is 20 C.
You have a slope of -35 and a point (20,2900)
So, 2900 = -35(20)+b
b = 2900 + 700 = 3600
Therefore equation is:
Calories used = -35(temperature) + 3600
-------
Sahara question:
Cals used = -35(50)+3600 = -1750+3600 = 1850
-----------------
in Antarctica in August when the temp is -50 C.
Antartica question:
Cals used = -36(-50)+3600 = 1800+3600 = 6400 calories
------------------
---------------
c) At what temp does your model predict that a working person would use no calories at all.
0 = -35x + 3600
-35x = -3600
x = 102.87 C
-----------------
d) Do you think the linear function gives meaningful answers for temp this hot?
No.
--------------
e) Sketch a graph of the function using a reasonable domain.

==============
Cheers,
Stan H.

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