Maths-
General
Easy

Question

Between 1985 and 2003, data were collected every three years on the amount of plastic produced annually in the United States, in billions of pounds. The graph below shows the data and a line of best fit. The equation of the line of best fit is y equals 3.39 x plus 46.89 , where x  is the number of years since 1985 and y is the amount of plastic produced annually, in billions of pounds.

Which of the following is the best interpretation of the number 3.39 in the context of the problem?

  1. The amount of plastic, in billions of pounds, produced in the United States during the year 1985
  2. The number of years it took the United States to produce 1 billion pounds of plastic
  3. The average annual plastic production, in billions of pounds, in the United States from 1985 to 2003
  4. The average annual increase, in billions of pounds, of plastic produced per year in the United States from 1985 to 2003

hintHint:

According to the line of best fit equation, y = ax + c, where y is the predicted value, a is the increment rate for the independent variable x and c is a constant which particularly represents the initial value. We take up this concept and interpret the problem statement to solve it.

The correct answer is: The average annual increase, in billions of pounds, of plastic produced per year in the United States from 1985 to 2003


    Step 1 of 2:
    The equation of the line of best fit is given by, y = 3.39x + 46.89
    Comparing the above equation with the general form of a best fitted line stated in the hint section, we get a = 3.39 and c = 46.89
    Step 2 of 2:
    As the concept explained in the hint section, the component a represents the increment rate of the independent variable x.
    Hence, the number 3.39 represents the rate of increase of plastic produced per year.
    Final Answer:
    The best interpretation is— D) The average annual increase, in billions of pounds, of plastic produced per year in the United States from 1985 to 2003.

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