Question 107512
Cricket Problem: Based on information in Deep River Jim's Wilderness Trailbook, the rate at which crickets chirp is a lenear function of temperature. At 55 degrees F they make 70 chirps per minute and at 69 degrees F they make 126 chirps per minute.
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You have two points: (55,70) and (69,126)
a) Write the equation expressing chirping rate as a function of temperature.
slope = [126-70]/[69-55] = 56/14 = 4
chirps = slope(temp) + b
Substitute chirps=70,temp=55,slope=4 to solve for "b":
70 = 4(55)+b
b = -150
EQUATION: chirps = 4(temp)-150
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b) Predict the chirping rate at 90 degrees F.
chirps = 4*90-150
chirps = 360-150
chirps = 210
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c) How warm is it if they are chirping 120 chirps per minute?
120 = 4*temp - 150
270 = 4*temp
temp = 135/2 = 67.5 degrees
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d) Calculate the temperature-intercept. What does this tell you about this number in the real-world?
temp-intercept = -150
It is unrealistic as it occurs when the termperature is zero.
Of course there are no crickets around when the temp is zero.
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e) Calculate the chirping-intercept. What does the chirping-intercept tell you about the real-world?
nothing
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f) Shetch and label the graph.
Plot the two points and draw a line thru them.
{{{graph(400,300,-10,100,-160,160,4x-150)}}}
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Cheers,
Stan H.