Thank you for visiting The owner of a coffee shop wants to compare how much coffee and tea he serves over a six hour period At the end of. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To find the function rule that describes the relationship between the number of cups of coffee, [tex]\(c\)[/tex], and the number of cups of tea, [tex]\(t\)[/tex], we need to identify a consistent relationship between the two.
Looking at the table of values:
- When [tex]\( t = 1 \)[/tex], [tex]\( c = 6 \)[/tex]
- When [tex]\( t = 3 \)[/tex], [tex]\( c = 12 \)[/tex]
- When [tex]\( t = 5 \)[/tex], [tex]\( c = 18 \)[/tex]
- When [tex]\( t = 7 \)[/tex], [tex]\( c = 24 \)[/tex]
- When [tex]\( t = 9 \)[/tex], [tex]\( c = 30 \)[/tex]
- When [tex]\( t = 11 \)[/tex], [tex]\( c = 36 \)[/tex]
We can observe that as the number of cups of tea increases by 2, the number of cups of coffee increases by 6. This suggests a linear relationship, where the change in coffee cups is directly proportional to the change in tea cups.
The pattern shows that for every increase of 1 cup of tea, the cups of coffee increase by 6.
Thus, we can express this relationship with the function rule:
[tex]\[ c = 6t + B \][/tex]
To find [tex]\( B \)[/tex], we can pick one pair from the table. Using [tex]\( t = 1 \)[/tex] and [tex]\( c = 6 \)[/tex]:
[tex]\[ 6 = 6(1) + B \][/tex]
[tex]\[ 6 = 6 + B \][/tex]
[tex]\[ B = 0 \][/tex]
So, the function rule that best describes the relationship is:
[tex]\[ c = 6t + 0 \][/tex]
Therefore, the function rule simplifies to:
[tex]\[ c = 6t \][/tex]
Looking at the table of values:
- When [tex]\( t = 1 \)[/tex], [tex]\( c = 6 \)[/tex]
- When [tex]\( t = 3 \)[/tex], [tex]\( c = 12 \)[/tex]
- When [tex]\( t = 5 \)[/tex], [tex]\( c = 18 \)[/tex]
- When [tex]\( t = 7 \)[/tex], [tex]\( c = 24 \)[/tex]
- When [tex]\( t = 9 \)[/tex], [tex]\( c = 30 \)[/tex]
- When [tex]\( t = 11 \)[/tex], [tex]\( c = 36 \)[/tex]
We can observe that as the number of cups of tea increases by 2, the number of cups of coffee increases by 6. This suggests a linear relationship, where the change in coffee cups is directly proportional to the change in tea cups.
The pattern shows that for every increase of 1 cup of tea, the cups of coffee increase by 6.
Thus, we can express this relationship with the function rule:
[tex]\[ c = 6t + B \][/tex]
To find [tex]\( B \)[/tex], we can pick one pair from the table. Using [tex]\( t = 1 \)[/tex] and [tex]\( c = 6 \)[/tex]:
[tex]\[ 6 = 6(1) + B \][/tex]
[tex]\[ 6 = 6 + B \][/tex]
[tex]\[ B = 0 \][/tex]
So, the function rule that best describes the relationship is:
[tex]\[ c = 6t + 0 \][/tex]
Therefore, the function rule simplifies to:
[tex]\[ c = 6t \][/tex]
Thank you for reading the article The owner of a coffee shop wants to compare how much coffee and tea he serves over a six hour period At the end of. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
- You are operating a recreational vessel less than 39 4 feet long on federally controlled waters Which of the following is a legal sound device
- Which step should a food worker complete to prevent cross contact when preparing and serving an allergen free meal A Clean and sanitize all surfaces
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees
Rewritten by : Jeany
