1. Ten year old Kayla's lemonade stand has experienced rises and falls in sales caused by temperature changes over the last few weeks. Her sales over the first few weeks of the summer were stacked according to the model S(x) = 2x³ - 32x² + 128x + 6¹, where x is the number of weeks and S(x) is the number of sales. a) Kayla makes a profit if she sells at least 6 glasses of lemonade. Use the model to determine the number of days that she made a profit. b) What are the domain and range? Interpret each. c) Predict the number of sales on her last week of sales (Assume 12 weeks). Does this seem reasonable? What kind of conclusions would you make about the weather with this model?
1. Ten year old Kayla's lemonade stand has experienced rises and falls in sales caused by temperature changes over the last few weeks. Her sales over the first few weeks of the summer were stacked according to the model S(x) = 2x³ - 32x² + 128x + 6¹, where x is the number of weeks and S(x) is the number of sales. a) Kayla makes a profit if she sells at least 6 glasses of lemonade. Use the model to determine the number of days that she made a profit. b) What are the domain and range? Interpret each. c) Predict the number of sales on her last week of sales (Assume 12 weeks). Does this seem reasonable? What kind of conclusions would you make about the weather with this model?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Ten year old Kayla's lemonade stand has experienced rises and falls in sales caused
by temperature changes over the last few weeks. Her sales over the first few weeks of
the summer were stacked according to the model S(x) =2x³ – 32x2 + 128x + 6 ,
where x is the number of weeks and S(x) is the number of sales.
a) Kayla makes a profit if she sells at least 6 glasses of lemonade. Use the model
to determine the number of days that she made a profit.
b) What are the domain and range? Interpret each.
c) Predict the number of sales on her last week of sales (Assume 12 weeks). Does
this seem reasonable? What kind of conclusions would you make about the
weather with this model?
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