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Let D(p) be the number of iced cappuccinos sold each week by a coffeehouse when the price is p cents.

a) What does the expression D(225) represent?

b) Do you think that D(p) is an increasing function or a decreasing function? Why?

c) What does the following equation tell you about p? D(p)=180

d) The coffeehouse sells n iced cappuccinos when they charge the average price in their area,
t cents. Thus, D(t)=n . What is the meaning of the following expressions: D(1.5t), 1.5D(t), D(t+50), D(t)+50?

User ParkerD
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a) The expression D(225) represents the number of iced cappuccinos sold each week by a coffeehouse when the price is 225 cents.

b) Whether D(p) is an increasing or decreasing function depends on the relationship between the price of iced cappuccinos and the number sold. If the price of iced cappuccinos increases, the number sold may decrease (decreasing function) or if the price of iced cappuccinos decreases, the number sold may increase (increasing function) . It's possible that the coffeehouse has made a market research and they know what is the best price for their iced cappuccinos.

c) The equation D(p) = 180 tells you that the coffeehouse sells 180 iced cappuccinos each week when the price is p cents.

d) D(1.5t) represents the number of iced cappuccinos sold each week when the price is 1.5t (1.5 times the average price in the area). 1.5D(t) represents the number of iced cappuccinos sold each week when the price is the average price in the area multiplied by 1.5. D(t+50) represents the number of iced cappuccinos sold each week when the price is t+50 (50 cents more than the average price in the area). D(t)+50 represents the number of iced cappuccinos sold each week when the price is the average price in the area plus 50.

It's important to note that all these expressions doesn't give us any information about the relation between price and quantity sold, they just give us the value of the function for specific values of p.

User Vijay Kumbhani
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