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The following table shows actual and projected worldwide annual sales and average selling prices of a certain type of smartphone in 2020 and 2024.Year 2020 2024Selling Price ($) 550 350Sales (millions) 210 770(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 (in millions) if the price is lowered to $300. million phones(b)Fill in the blank.For every $1 increase in price, sales of this type of cell phone decrease by million units.

Question

The following table shows actual and projected worldwide annual sales and average selling prices of a certain type of smartphone in 2020 and 2024.Year 2020 2024Selling Price ()550350Sales(millions)210770(a)Usethedatatoobtainalineardemandfunctionforthistypeofcellphone.(Letpbetheprice,andletqbethedemand).q(p)=Useyourdemandequationtopredictsales(inmillions)ifthepriceisloweredto) 550 350Sales (millions) 210 770(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 (in millions) if the price is lowered to 300. million phones(b)Fill in the blank.For every $1 increase in price, sales of this type of cell phone decrease by million units.

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Solution

(a) To obtain a linear demand function, we first need to find the slope of the line that connects the two points (p1, q1) and (p2, q2), where p is the price and q is the demand. The two points given are (550, 210) and (350, 770).

The formula for the slope (m) is (q2 - q1) / (p2 - p1). Substituting the given values, we get:

m = (770 - 210) / (350 - 550) = 560 / -200 = -2.8

This means that for every $1 decrease in price, the demand increases by 2.8 million units.

The demand function has the form q(p) = mp + b, where b is the y-intercept. To find b, we can substitute one of the points into the equation. Let's use (550, 210):

210 = -2.8 * 550 + b b = 210 + 2.8 * 550 = 1690

So, the demand function is q(p) = -2.8p + 1690.

To predict the sales if the price is lowered to $300, we substitute p = 300 into the demand function:

q(300) = -2.8 * 300 + 1690 = 2530 million phones.

(b) For every $1 increase in price, sales of this type of cell phone decrease by 2.8 million units.

This problem has been solved

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