DATA ANALYSIS: TEMPERATURE The table shows the temperatures...

DATA ANALYSIS: TEMPERATURE The table shows the temperatures $y$ (in degrees Fahrenheit) in a certain city over a 24-hour period. Let $x$ represent the time of day, where $x=0$ corresponds to 6 A.M. A model that represents these data is given by $y = 0.026x^3 - 1.03x^2 + 10.2x + 34$, $0 \leq x \leq 24$. (a) Use a graphing utility to create a scatter plot of the data. Then graph the model in the same viewing window. (b) How well does the model fit the data? (c) Use the graph to approximate the times when the temperature was increasing and decreasing. (d) Use the graph to approximate the maximum and minimum temperatures during this 24-hour period. (e) Could this model be used to predict the temperatures in the city during the next 24-hour period? Why or why not?

DATA ANALYSIS: TEMPERATURE The table shows the temperatures $y$ (in degrees Fahrenheit) in a certain city over a 24-hour period. Let $x$ represent the time of day, where $x=0$ corresponds to 6 A.M.

A model that represents these data is given by

$y = 0.026x^3 - 1.03x^2 + 10.2x + 34$, $0 \leq x \leq 24$.

(a) Use a graphing utility to create a scatter plot of the data. Then graph the model in the same viewing window.

(b) How well does the model fit the data?

(c) Use the graph to approximate the times when the temperature was increasing and decreasing.

(d) Use the graph to approximate the maximum and minimum temperatures during this 24-hour period.

(e) Could this model be used to predict the temperatures in the city during the next 24-hour period? Why or why not?

Transcript

00:01 I'm going to use a graph and calculator to do this problem.

00:04 So first of all, we have a table of data, and we want to make a scatter plot.

00:08 So we go to stat and then edit, and we type all of the data into list one and list two, as you see i've already done.

00:16 So in the first list, we have the x values.

00:18 Those are the times.

00:20 And in the second list, we have the y values.

00:22 Those are the temperatures.

00:24 Now to get a scatter plot, what we can do is we can go into second y equals, which takes us to the stat plot menu.

00:31 Press enter to go into the menu for plot one, turn it on, and make sure it's scatterplot using list one and list two.

00:39 Now to get a good window, we go into the zoom menu and we go down to zoom 9, which is zoom stat, and the calculator will figure out a window for us.

00:50 Okay, the scatter plot is just the points that were plotted, not the curve that you see going now.

00:55 The curve is jumping ahead of me a little bit.

00:58 So the curve is the model, the equation that was given in the problem, was the cubic equation and i typed it into my y equals menu and then we see it plotted against the scatter plot.

01:12 So for part b, how well does the model fit the data? that model fits the data extremely well.

01:17 We see it touching all of those points in the scatter plot.

01:19 So that's a good thing.

01:21 Now using this model, we're going to approximate the times when the temperature is increasing and decreasing.

01:26 So i'm going to press trace.

01:28 And then i'm going to press the down arrow and now my cursor is on the model, not on the scatter plot.

01:33 So it's on the curve itself.

01:34 And what i'm going to do is move my cursor over to the left until it gets to right about the top point there...

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