6. Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade you sell 100 cups. But when you raise your price to $4 you only sell 50 cups. Write an equation for the number of cups you sell as a function of the price you charge. Denote "C" for number of cups, and "P" for the price you charge. Assume the function is linear.
From the data, C*P=200
C= 200/P
One can assume all one wants, but the funcion is not linear.
To find the equation for the number of cups you sell as a function of the price you charge, we need to determine the equation of a straight line that passes through two given points: (100, 2) and (50, 4).
We can use the slope-intercept form of a linear equation, which is given by:
y = mx + b
where y is the dependent variable (number of cups), x is the independent variable (price), m is the slope, and b is the y-intercept.
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (100, 2) and (50, 4):
m = (4 - 2) / (50 - 100)
= 2 / (-50)
= -0.04
Now, we can substitute one of the points and the slope into the slope-intercept form to find the y-intercept (b).
Using the point (100, 2):
2 = (-0.04)(100) + b
2 = -4 + b
b = 2 + 4
= 6
Therefore, the equation for the number of cups you sell (C) as a function of the price you charge (P) is:
C = -0.04P + 6
To write the equation for the number of cups you sell as a function of the price you charge, we can use the formula for a line in slope-intercept form: y = mx + b.
In this case, let "C" represent the number of cups sold and "P" represent the price charged. We are given two points on the line: (100, 2) and (50, 4).
First, we need to find the slope (m) of the line. The slope is calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points: (100, 2) and (50, 4):
Substituting the values:
m = (4 - 2) / (50 - 100)
Simplifying:
m = 2 / (-50)
m = -0.04
Next, we need to find the y-intercept (b) of the line. We can use the slope-intercept form of the line equation and substitute one of the given points:
y = mx + b
2 = (-0.04)(100) + b
Simplifying:
2 = -4 + b
b = 6
Therefore, the equation for the number of cups sold as a function of the price charged is:
C = -0.04P + 6