A movie theater finds that by changing the price on a small bag of popcorn, they...

   

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A movie theater finds that by changing the price on a small bag of popcorn, they will change the number of bags they sell during a movie. Cost ($) # of bags sold during movie $1.90 100 $1.95 95 $2.00 90 $2.05 85 $2.10 80 $2.15 75 1. What relationships do you notice between the cost and the amount of pop- corn the theater sells? 2. Explain why these relationships seems reasonable (or unreasonable). 3. Is the information in the table above sufficient to determine the price that theaters should choose for a bag of popcorn? Explain your reasoning. 4. Suppose it costs the theater $1.25 to make and sell a small bag of popcorn. Make a third column in the table above that shows the amount of profit the the- ater makes for each selling price. Based on this, what would be the best price for the theaters to choose? Because it seems that the number of bags sold depends on the cost of a bag, we could use function notation to describe the data in the above table. For exam- ple, to say that "If the cost is $2.10, the theater will sell 80 bags of popcorn," we could write B($2.10)=80, where B represents the number of bags sold at the price (given in parentheses). Note that whenever you begin using a variable to represent something, you should let others know what that variable means. Because we have already stated what B stands for, you may continue to use it without needing to specify its meaning. 5. Use functional notation to represent each of the following sentences. a. When a bag of popcorn costs $1.90, 100 bags of popcorn will be sold. b. The theater only sells 75 bags when the cost is raised to $2.15. 6. Use functional notation to show the number of bags you think would be sold if the cost were raised to $2.40. A movie theater finds that by changing the price on a small bag of popcorn, they will change the number of bags they sell during a movie. Cost ($) # of bags sold during movie $1.90 100 $1.95 95 $2.00 90 $2.05 85 $2.10 80 $2.15 75 1. What relationships do you notice between the cost and the amount of pop- corn the theater sells? 2. Explain why these relationships seems reasonable (or unreasonable). 3. Is the information in the table above sufficient to determine the price that theaters should choose for a bag of popcorn? Explain your reasoning. 4. Suppose it costs the theater $1.25 to make and sell a small bag of popcorn. Make a third column in the table above that shows the amount of profit the the- ater makes for each selling price. Based on this, what would be the best price for the theaters to choose? Because it seems that the number of bags sold depends on the cost of a bag, we could use function notation to describe the data in the above table. For exam- ple, to say that "If the cost is $2.10, the theater will sell 80 bags of popcorn," we could write B($2.10)=80, where B represents the number of bags sold at the price (given in parentheses). Note that whenever you begin using a variable to represent something, you should let others know what that variable means. Because we have already stated what B stands for, you may continue to use it without needing to specify its meaning. 5. Use functional notation to represent each of the following sentences. a. When a bag of popcorn costs $1.90, 100 bags of popcorn will be sold. b. The theater only sells 75 bags when the cost is raised to $2.15. 6. Use functional notation to show the number of bags you think would be sold if the cost were raised to $2.40.