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Thread: Algebra 1 Story Problem?

  1. #1

    Algebra 1 Story Problem?

    *I have asked countless people to help me with this story problem and nobody seems to know how to do it! Please help!


    Natalie performs a chemistry experiment where she records the temperature of an ongoing reaction. The solution is 93.5º C after 3 minutes; 90º C after 5 minutes, 84.8 C after 9 minutes; 70.2º C after 18 minute; 54.4º C after 30 minutes; 42.5ºC after 37 minutes; and 24.9º C after 48 minutes. Perform a linear regression on this data to complete the following items.


    1.) What does the value of the correlation coefficient tell you about correlation of the data?


    2.) Write the equation of the best-fitting line. (Round to the nearest thousandths.)


    3.) On average, how much does the temperature decrease every five minutes?


    4.) If Natalie's solution is expected to freeze at -7º C, how many minutes into the experiment should the solution freeze? (Show work that supports your prediction).

  2. #2
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    Quote Originally Posted by ronya12 View Post
    *I have asked countless people to help me with this story problem and nobody seems to know how to do it! Please help!


    Natalie performs a chemistry experiment where she records the temperature of an ongoing reaction. The solution is 93.5º C after 3 minutes; 90º C after 5 minutes, 84.8 C after 9 minutes; 70.2º C after 18 minute; 54.4º C after 30 minutes; 42.5ºC after 37 minutes; and 24.9º C after 48 minutes. Perform a linear regression on this data to complete the following items.


    1.) What does the value of the correlation coefficient tell you about correlation of the data?


    2.) Write the equation of the best-fitting line. (Round to the nearest thousandths.)


    3.) On average, how much does the temperature decrease every five minutes?


    4.) If Natalie's solution is expected to freeze at -7º C, how many minutes into the experiment should the solution freeze? (Show work that supports your prediction).
    We do not (generally) provide answers. We provide help so that you can find the answer yourself. After all, we are not the ones who will have to take the final exam.

    First off, are you in high school or college? What class are you taking?

    How have you been taught to do a linear regression? Spreadsheet, scientific calculator, by hand?

    What would your independent variable or variables be?

    What would your dependent variable be?

  3. #3
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    Quote Originally Posted by ronya12 View Post
    *I have asked countless people to help me with this story problem and nobody seems to know how to do it! Please help!


    Natalie performs a chemistry experiment where she records the temperature of an ongoing reaction. The solution is 93.5º C after 3 minutes; 90º C after 5 minutes, 84.8 C after 9 minutes; 70.2º C after 18 minute; 54.4º C after 30 minutes; 42.5ºC after 37 minutes; and 24.9º C after 48 minutes. Perform a linear regression on this data to complete the following items.


    1.) What does the value of the correlation coefficient tell you about correlation of the data?


    2.) Write the equation of the best-fitting line. (Round to the nearest thousandths.)


    3.) On average, how much does the temperature decrease every five minutes?


    4.) If Natalie's solution is expected to freeze at -7º C, how many minutes into the experiment should the solution freeze? (Show work that supports your prediction).
    Put simply, you have been given a series of points. (Since temperatures are dropping during the reaction, it would appear that an endothermic reaction is being described. However, the fact that they are given with temperatures in degrees C instead of Kelvins indicates we are not really examining the energy of a system, so our model may not reflect reality. Regardless…) Since we see that temperature depends on time, we list time first, i.e., time is on the x-axis, and temperature is on the y-axis. The points are:


    (3. 93.5) (5, 90) (9, 84.8) (18, 70.2) (30, 54.4) (37, 42.5) (48, 24.9)

    Plot them on a graph of Temperature vs Time.


    If you are using a calculator or other software (which must be the case since you are told to "round to the nearest thousandth"), enter these data points into it and analyze them using "linear regression" mode or "least squares regression" or some such.

    Study your calculator's manual to find out how to do this and also how to interpret the output, i.e., what the variables in your output stand for.

    That's it; you just have to learn how to use your calculator.

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