A manufacturer of graphing calculators has determined that 10,000 calculators per week will be sold at a price of $95 per calculator. At a price of $90, it is estimated that 14,000 calculators will be sold. Determine a linear function that predicts the number of calculators y that will be sold per week at a price of x dollars.
y =
Use this model to predict the number of calculators that will be sold at a price of $65.
calculators
y = -800x + 74,000
With x = $65:
y = -800(65) + 74,000
y = -52,000 + 74,000
y = 22,000
Therefore, the model predicts that 22,000 calculators will be sold at a price of $65.
show your work
To determine the linear function that predicts the number of calculators sold per week at a given price, we can use the two data points provided:
Point 1: (95, 10,000)
Point 2: (90, 14,000)
First, we need to find the slope (m) of the line using the two points:
m = (y2 - y1) / (x2 - x1)
m = (14,000 - 10,000) / (90 - 95)
m = 4,000 / (-5)
m = -800
Next, we can use the point-slope form of a linear equation to find the linear function:
y - y1 = m(x - x1)
Using point (95, 10,000) as our reference point:
y - 10,000 = -800(x - 95)
y - 10,000 = -800x + 76,000
y = -800x + 86,000
So, the linear function that predicts the number of calculators sold per week at a price of x dollars is y = -800x + 86,000.
To predict the number of calculators that will be sold at a price of $65:
y = -800(65) + 86,000
y = -52,000 + 86,000
y = 34,000
Therefore, the model predicts that 34,000 calculators will be sold at a price of $65.