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Tyler Tortoise, who has grown a 4 mm beard prior to applying the hair treatment, applies the product he purchased and determines that the length of his beard can be found using the following table with y being the total length in mm on any given day, and x being the number of days. # of Days 4 6 Total Length mm 4 4.5 5.5 Which tortoise bought the hair product that causes hair to grow the fastest? Explain your reasoning. Use equations, tables, and graphs.

Tyler Tortoise, who has grown a 4 mm beard prior to applying the hair treatment, applies the product he purchased and determines that the length of his beard can be found using the following table with y being the total length in mm on any given day, and x being the number of days. # of Days 4 6 Total Length mm 4 4.5 5.5 Which tortoise bought the hair product that causes hair to grow the fastest? Explain your reasoning. Use equations, tables, and graphs.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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You may have read Aesop's Fable, The Tortoise and The Hare. But have you ever heard the story of The Tortoises' Hair? This is a story about 3 teenage tortoises trying to grow their facial hair. Together the three watch TV infomercials for hair-growing treatments, and are torn between which to buy, so each tortoise chooses one product to test. Tommy Tortoise, who has grown a 3mm beard prior to buying the product, applies the product he purchased and determines that the length of his beard can be found by the equation y = 1/5 x + 3 with y being the total length in mm, and x being the number of days the product is applied. Teddy Tortoise, who prior to the purchase has grown a 5 mm beard, applies the product he purchased and determines that the daily length of his beard can be found using the following graph. --- The graph below shows the relationship between the number of days the product is applied (x-axis) and the length of the beard in mm (y-axis). - The x-axis is labeled "Number of Days" and ranges from 0 to 25. - The y-axis is labeled "Length in mm" and ranges from 0 to 20. The graph depicts a linear relationship where the length of the beard increases steadily over time. The starting point of the graph indicates that the initial length of Teddy Tortoise's beard is 5 mm. The line then extends upward, showing incremental growth as the days progress.
Transcribed Image Text:You may have read Aesop's Fable, The Tortoise and The Hare. But have you ever heard the story of The Tortoises' Hair? This is a story about 3 teenage tortoises trying to grow their facial hair. Together the three watch TV infomercials for hair-growing treatments, and are torn between which to buy, so each tortoise chooses one product to test. Tommy Tortoise, who has grown a 3mm beard prior to buying the product, applies the product he purchased and determines that the length of his beard can be found by the equation y = 1/5 x + 3 with y being the total length in mm, and x being the number of days the product is applied. Teddy Tortoise, who prior to the purchase has grown a 5 mm beard, applies the product he purchased and determines that the daily length of his beard can be found using the following graph. --- The graph below shows the relationship between the number of days the product is applied (x-axis) and the length of the beard in mm (y-axis). - The x-axis is labeled "Number of Days" and ranges from 0 to 25. - The y-axis is labeled "Length in mm" and ranges from 0 to 20. The graph depicts a linear relationship where the length of the beard increases steadily over time. The starting point of the graph indicates that the initial length of Teddy Tortoise's beard is 5 mm. The line then extends upward, showing incremental growth as the days progress.
**Title: Observing Beard Growth in Tortoises using Hair Treatment Products** **Introduction:** Tyler Tortoise, who initially has a 4 mm beard, decided to apply a hair treatment product he purchased to observe its effect on the growth of his beard. He meticulously recorded the growth over a period, noting the total length (in mm) over several days. The following table illustrates the relationship between the number of days (x) and the total length of his beard (y) in mm. **Data Table:** | # of Days | 0 | 2 | 4 | 6 | |-----------|----|-----|----|-----| | Total Length (mm) | 4 | 4.5 | 5 | 5.5 | **Interpreting the Data:** From the table, we can observe the following: - On day 0, Tyler's beard length is 4 mm. - On day 2, the beard has grown to 4.5 mm. - On day 4, the beard reaches 5 mm. - By day 6, the beard length is 5.5 mm. **Discussion:** To determine which tortoise (hypothetically comparing Tyler's data with another tortoise's result not provided here) bought the most effective hair treatment product that accelerates beard growth the fastest, we analyze the rate of growth. **Analysis Using Equations and Graphs:** 1. **Linear Growth Equation:** The increase in beard length over time suggests a linear relationship: Since the change in length per day is consistent (0.25 mm/day), we can model Tyler's beard growth using the equation: \[ y = 4 + 0.25x \] where \( y \) represents the total beard length in mm and \( x \) represents the number of days. 2. **Graphical Representation:** Plotting the data points on a graph with the x-axis representing the number of days and the y-axis representing the total beard length in mm demonstrates a straightforward linear increase. **Conclusion:** To conclude which tortoise used the fastest hair growth product, one would compare the slope of the line formed by the data points. A steeper slope would indicate faster growth. Using the example provided, Tyler Tortoise's beard grows at a rate of 0.25 mm per day. **
Transcribed Image Text:**Title: Observing Beard Growth in Tortoises using Hair Treatment Products** **Introduction:** Tyler Tortoise, who initially has a 4 mm beard, decided to apply a hair treatment product he purchased to observe its effect on the growth of his beard. He meticulously recorded the growth over a period, noting the total length (in mm) over several days. The following table illustrates the relationship between the number of days (x) and the total length of his beard (y) in mm. **Data Table:** | # of Days | 0 | 2 | 4 | 6 | |-----------|----|-----|----|-----| | Total Length (mm) | 4 | 4.5 | 5 | 5.5 | **Interpreting the Data:** From the table, we can observe the following: - On day 0, Tyler's beard length is 4 mm. - On day 2, the beard has grown to 4.5 mm. - On day 4, the beard reaches 5 mm. - By day 6, the beard length is 5.5 mm. **Discussion:** To determine which tortoise (hypothetically comparing Tyler's data with another tortoise's result not provided here) bought the most effective hair treatment product that accelerates beard growth the fastest, we analyze the rate of growth. **Analysis Using Equations and Graphs:** 1. **Linear Growth Equation:** The increase in beard length over time suggests a linear relationship: Since the change in length per day is consistent (0.25 mm/day), we can model Tyler's beard growth using the equation: \[ y = 4 + 0.25x \] where \( y \) represents the total beard length in mm and \( x \) represents the number of days. 2. **Graphical Representation:** Plotting the data points on a graph with the x-axis representing the number of days and the y-axis representing the total beard length in mm demonstrates a straightforward linear increase. **Conclusion:** To conclude which tortoise used the fastest hair growth product, one would compare the slope of the line formed by the data points. A steeper slope would indicate faster growth. Using the example provided, Tyler Tortoise's beard grows at a rate of 0.25 mm per day. **
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