Suppose the number of hours of sleep you obtain, s, is a linear function of the number of caffeinated beverages you drink, n. Furthermore, you have collected data to show that if you drink 3 caffeinated beverages you obtain 7 hours of sleep; whereas, if you drink 12 caffeinated beverages you obtain 1 hour of sleep. Find a formula for this linear function. Be careful to identify which variable is the independent variable. Show or explain your work. Interpret the slope within the context of this problem.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Suppose the number of hours of sleep you obtain, s, is a linear function of the number of caffeinated beverages you drink, n. Furthermore, you have collected data to show that if you drink 3 caffeinated beverages you obtain 7 hours of sleep; whereas, if you drink 12 caffeinated beverages you obtain 1 hour of sleep.

  1. Find a formula for this linear function. Be careful to identify which variable is the independent variable. Show or explain your work. 
  2. Interpret the slope within the context of this problem.
Expert Solution
Step 1: given information

The number of hours of sleep obtain, s, is a linear function of the number of caffeinated beverages drink, n.

 If you drink 3 caffeinated beverages obtain 7 hours of sleep; whereas, if drink 12 caffeinated beverages obtain 1 hour of sleep.


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