In 1972, there were 3.4 trillion cigarettes purchased worldwide, and in 1984, there were 4.3 trillion cigarettes purchased worldwide(in trillions) in the year x, where x=0 represents the year 1972.
(a) Which of the following linear equations could be used to predict the number of trillions of cigarettes y purchased worldwide in a given year x, where x=0 represents the year 1972?
A. y=3.4x+4.3
B. y=0.9x-6.5
C. y=0.9x+3.4
D. y=0.075x+3.4
(b) Use the equation form part (a) to estimate the number of cigarettes purchased worldwide in the year 2008.
(c) Fill in the blanks to interpret the slop of the equation: The rate of change of cigarettes purchased worldwide with respect to time is _______ per_____. (include units of measurement.)
a) If x = 0 represents the year 1972, then x = 12 represents 1984.
If x = 0 or x = 12, the equation that fits would be D (substituting those two values for x and solving for y).
b) If x = 0 represents the year 1972, then x = 36 represents the year 2008. Substitute 36 for x in the equation and solve for y.
c) I'll let you figure out this one.
To find the linear equation that can be used to predict the number of trillions of cigarettes purchased worldwide in a given year, we need to analyze the given information.
In 1972, there were 3.4 trillion cigarettes purchased. This means that when x=0 (representing the year 1972), y (the number of cigarettes) is 3.4 trillion. Similarly, in 1984, there were 4.3 trillion cigarettes purchased. This means that when x=12 (representing the year 1984, 12 years after 1972), y=4.3 trillion.
We can use this information to find the equation by calculating the slope and the y-intercept.
Slope (m) = (change in y)/(change in x) = (4.3 - 3.4)/(12 - 0) = 0.9/12 = 0.075
Therefore, the slope of the equation is 0.075.
Now, let's substitute the values of x and y in one of the given equations to see which one satisfies the given data.
(a) y = 3.4x + 4.3
Substituting x=0 and y=3.4:
3.4 = 3.4(0) + 4.3
3.4 = 4.3
The equation does not satisfy the given data, so it is not the correct equation.
(b) y = 0.9x - 6.5
Substituting x=12:
y = 0.9(12) - 6.5
y ≈ 10.8 - 6.5
y ≈ 4.3
The equation satisfies the given data, so it can be used to predict the number of cigarettes purchased worldwide.
(c) The slope of the equation represents the rate of change of cigarettes purchased worldwide with respect to time. In this case, the slope is 0.075. The slope can be interpreted as the increase in the number of cigarettes purchased worldwide per year. Therefore, the rate of change is 0.075 trillion cigarettes per year.