Question

Biologists have found that the number of chirps some crickets make per minute is related to temperature. The relationship is very close to being linear. When crickets chirp 124 times a minute, it is about 68 degrees Fahrenheit. When they chirp 172 times a minute, it is about 80 degrees Fahrenheit. Let the number of chirps be C and the temperature in degrees Fahrenheit be F. a) Find an equation for the line that models this situation. b) How warm is it when the crickets are chirping 150 times a minute? c) Identify the slope, C-intercept, and F-intercept. d) Interpret the meaning of slope, C-intercept, and F-intercept. e) Sketch the calculated equation.

          Biologists have found that the number of chirps some crickets make per minute is related to temperature. The relationship is very close to being linear. When crickets chirp 124 times a minute, it is about 68 degrees Fahrenheit. When they chirp 172 times a minute, it is about 80 degrees Fahrenheit. Let the number of chirps be C and the temperature in degrees Fahrenheit be F.

a) Find an equation for the line that models this situation.
b) How warm is it when the crickets are chirping 150 times a minute?
c) Identify the slope, C-intercept, and F-intercept.
d) Interpret the meaning of slope, C-intercept, and F-intercept.
e) Sketch the calculated equation.

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Added by Michelle B.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Suzanne W.

08/10/2022

Step 1

We are given two points that relate the number of chirps (C) to the temperature (F): - Point 1: (124, 68) - Point 2: (172, 80) Show more…

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Biologists have found that the number of chirps some crickets make per minute is related to temperature. The relationship is very close to being linear. When crickets chirp 124 times a minute, it is about 68 degrees Fahrenheit. When they chirp 172 times a minute, it is about 80 degrees Fahrenheit. Let the number of chirps be C and the temperature in degrees Fahrenheit be F. a) Find an equation for the line that models this situation. b) How warm is it when the crickets are chirping 150 times a minute? c) Identify the slope, C-intercept, and F-intercept. d) Interpret the meaning of slope, C-intercept, and F-intercept. e) Sketch the calculated equation.

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Transcript

00:02 Okay, so you're given two points.

00:07 When a cricket chirps 124 times, it is about 68 degrees fahrenheit.

00:15 So we're going to let degrees fahrenheit be on our x axis because it is independent.

00:22 Our dependent variable are the amount of chirps.

00:26 So it's 68, 124.

00:29 And then we have 80, 172.

00:33 So finding the slope, m is equal to y2 minus y1 over x2 minus x1, 172 minus 124 is 48.

00:50 A minus 68 is 12, so the slope is 4.

00:54 It's in the form y equals mx plus b, so this is 4x, and then we can plug in.

01:04 So i'm going to plug in, pick a value, either, the first set of points are the second set of points.

01:09 I'm going to pick the second set of points.

01:12 So 172 for y, 4 for m, 80 for x.

01:19 That may be equal to negative 148.

01:23 That is the y intercept.

01:25 So y is equal to 4x minus 148.

01:30 I'm going to go ahead and answer another part.

01:34 So that's an equation.

01:36 We'll talk about part b and a second.

01:38 Part c, identify the slope.

01:40 The slope is four.

01:43 So let me grab in yellow.

01:46 So the slope is four.

01:48 Identify the f intercept and the c intercept...

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