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 , 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?
- The amount of plastic, in billions of pounds, produced in the United States during the year 1985
- The number of years it took the United States to produce 1 billion pounds of plastic
- The average annual plastic production, in billions of pounds, in the United States from 1985 to 2003
- The average annual increase, in billions of pounds, of plastic produced per year in the United States from 1985 to 2003
Hint:
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.
Related Questions to study
Some building codes require that, for indoor stairways, the tread depth must be at least 9 inches and the riser height must be at least 5 inches. According to the riser-tread formula, which of the following inequalities represents the set of all possible values for the riser height that meets this code requirement?
When designing a stairway, an architect can use the riser-tread formula , where h is the riser height, in inches, and d is the tread depth, in inches. For any given stairway, the riser heights are the same and the tread depths are the same for all steps in that stairway.
The number of steps in a stairway is the number of its risers. For example, there are 5 steps in the stairway in the figure above. The total rise of a stairway is the sum of the riser heights as shown in the figure.
In mathematics, inequalities explain the relationship between two non-equal values. When two values are not equal, we frequently use the "not equal symbol ()" to indicate this. However, many inequalities are used to compare the values and determine whether they are less than or greater.
¶A relationship is considered to be an inequality if it involves two real numbers or algebraic expressions and uses the symbols ">"; "<"; "≥"; "≤. "
¶Since the tread depth, 'd' is at least 9 inches, and the riser height, 'h' is at least 5 inches, it follows that h ≥ 5, and d ≥ 9
respectively. Solving for d in the riser tread formula 2h + d = 25 gives d = 25 - 2h. Thus the first inequality, d ≥ 9, is equivalent to
25-2h ≥ 9.
Some building codes require that, for indoor stairways, the tread depth must be at least 9 inches and the riser height must be at least 5 inches. According to the riser-tread formula, which of the following inequalities represents the set of all possible values for the riser height that meets this code requirement?
When designing a stairway, an architect can use the riser-tread formula , where h is the riser height, in inches, and d is the tread depth, in inches. For any given stairway, the riser heights are the same and the tread depths are the same for all steps in that stairway.
The number of steps in a stairway is the number of its risers. For example, there are 5 steps in the stairway in the figure above. The total rise of a stairway is the sum of the riser heights as shown in the figure.
In mathematics, inequalities explain the relationship between two non-equal values. When two values are not equal, we frequently use the "not equal symbol ()" to indicate this. However, many inequalities are used to compare the values and determine whether they are less than or greater.
¶A relationship is considered to be an inequality if it involves two real numbers or algebraic expressions and uses the symbols ">"; "<"; "≥"; "≤. "
¶Since the tread depth, 'd' is at least 9 inches, and the riser height, 'h' is at least 5 inches, it follows that h ≥ 5, and d ≥ 9
respectively. Solving for d in the riser tread formula 2h + d = 25 gives d = 25 - 2h. Thus the first inequality, d ≥ 9, is equivalent to
25-2h ≥ 9.