Answer:
6772 muffins.
Explanation:
To write a linear model that represents the number of muffins sold x years after 2010, we need to find the equation of a straight line that relates the number of muffins sold (y) to the number of years (x) after 2010.
First, we need to determine the slope of the line. The slope represents the rate of change in the number of muffins sold per year. We can calculate the slope using the formula:
slope = (change in y) / (change in x)
In this case, the change in y is the difference in the number of muffins sold between 2015 and 2010, which is 7420 - 5800 = 1620. The change in x is the number of years between 2015 and 2010, which is 2015 - 2010 = 5.
So, the slope of the line is:
slope = (1620) / (5) = 324
Next, we need to determine the y-intercept of the line. The y-intercept represents the initial number of muffins sold when x is zero (in this case, at the start of 2010). We can determine the y-intercept by substituting the values of x and y from one of the given data points into the equation of the line.
Using the data point (x = 0, y = 5800), we have:
y = mx + b
5800 = 324(0) + b
5800 = b
Therefore, the y-intercept is 5800.
Now we can write the linear model equation using the slope-intercept form:
y = mx + b
Substituting the values we found, the equation becomes:
y = 324x + 5800
This equation represents the number of muffins (y) that the bakery sells x years after 2010.
Example: If we want to find the number of muffins sold 3 years after 2010, we can substitute x = 3 into the equation:
y = 324(3) + 5800
y = 972 + 5800
y = 6772
So, the bakery would sell approximately 6772 muffins 3 years after 2010.