Question

The following table shows worldwide sales of a certain type of cell phone and their average selling prices in 2012 and 2013.
Year 2012 2013
Selling Price ($) 375 325
Sales (millions) 958 1,228
(a)
Use the data to obtain a linear demand function for this type of cell phone. (Let p be the price, and let q be the demand).
q(p) =
Use your demand equation to predict sales if the price is lowered to $275.
[. ] million phones
(b)
Fill in the blank.
For every $1 increase in price, sales of this type of cell phone decrease by [. ]
million units.

Answer 1

The demand equation illustrates how the price and the quantity of an item are related

• The linear demand equation is: $q = -5.4p + 2983$
• If the price is lowered to $275, the sales is 1498
• For every $1 increase in price, sales of this type of cell phone decrease

(a) Obtain the linear demand equation

From the question, we have the following ordered pairs

(x, y) = {(375,958) and (325,1228)

Start by calculating the slope (m)

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$m = \frac{1228 - 958}{325 - 375}$

$m = \frac{270}{-50}$

$m = -5.4$

The linear demand equation is then calculated as:

$y =m(x - x_1) + y_1$

So, we have:

$q = -5.4(p - 375) +958$

$q = -5.4p + 2983$

When the price is $275, the sales is:

$q = -5.4 * 275 + 2983$

$q = 1498$

Interpret the demand equation

The demand equation means that:

For every $1 increase in price, sales of this type of cell phone decrease by $5.4

Read more about demand equations at:

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