The USDA reported that in 1990 each person in the United States consumed an average of 133 pounds of natural sweeteners. They al
so claim this amount has decreased by about 0.6 pounds each year. a. If 1990 could be considered year zero, which of the above numbers represents the slope and which represents the y intercept? b. What is the equation of the line of best fit using the slope and y-intercept above? c. Predict the average consumption of sweeteners per person for the year 2005.
The problem implies that we want to write the (average) amount of natural sweeteners consumed per person as a function of time. Let y represent the (average) amount of natural sweeteners consumed per person (in pounds), and let x represent the time measured in years since 1990. That is, x = 0 represents 1990. If y is a linear function of x, then we can use the slope-intercept form y = mx + b (where m is the slope and b is the y-intercept) to write the function.
The slope can be interpreted as the rate of change of y with respect to x, which in this case means the change in consumption of natural sweeteners per year. The statement that consumption has decreased by 0.6 pounds per year tells us that the slope is m = -0.6 Also, the y-intercept is the same as the y-value of the function when x = 0. (In our case, that means time 0, that is, 1990.) Therefore the y-intercept is b = 133. Hope that helps! Let me know if you have any further questions.
ar some point pattern A will have the same numbers as pattern B as it moves along like if you add 3 for 2 more times in pattern A it will have 24 and so on..
