A farmer finds there is a linear relationship between the number of bean stalks, n, she plants and the yield, y, each plant produces. When she plants 30 stalks, each plant yields 26 oz of beans. When she plants 34 stalks, each plant produces 24 oz of beans. Find a linear relationship in the form y = mn + b that gives the yield when n stalks are planted. y =

A farmer finds there is a linear relationship between the number of bean stalks, n, she plants and the yield, y, each plant produces. When she plants 30 stalks, each plant yields 26 oz of beans. When she plants 34 stalks, each plant produces 24 oz of beans. Find a linear relationship in the form y = mn + b that gives the yield when n stalks are planted. y =

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.3: Modeling Data With Linear Functions

Problem 2E: Cost of Adding Employees The following table shows the cost, in millions of dollars, to Walmart of...

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Sound Speed in Oceans Marine scientists use a linear model for the speed c of sound in the oceans as a function of the salinity S at a fixed depth and temperature. In the following table, one scientist recorded data for c and S at a depth of 500 meters and a temperature of 15 degrees Celsius. Here c is measured in meters per second and S in part per thousand. Salinity S Sound speed c 35.0 1515.36 35.6 1516.08 36.2 1516.80 36.8 1517.62 37.4 1518.24 a. Looking over the table, the scientist realizes that one of the entries for sound speed is in error. Which entry is it, and what is the correct speed? b. Explain in practical terms the meaning of the slope of the linear model for c in terms of S at the given depth and temperature. c. Calculate c39 and explain in practical terms what it means.
Cost of Adding Employees The following table shows the cost, in millions of dollars, to Walmart of adding the given number of employees to each of its superstores.14 E = number of new employees 1 2 3 4 C = cost 89.6 179.2 268.8 358.4 a. Find a linear model for the data in the table. b. Explain in practical terms the meaning of the slope of the linear model you found in part a.
Demand for Candy Bars In this problem you will determine a linear demand equation that describes the demand for candy bars in your class. Survey your classmates to determine what price they would be willing to pay for a candy bar. Your survey form might look like the sample to the left. a Make a table of the number of respondents who answered yes at each price level. b Make a scatter plot of your data. c Find and graph the regression line y=mp+b, which gives the number of respondents y who would buy a candy bar if the price were p cents. This is the demand equation. Why is the slope m negative? d What is the p-intercept of the demand equation? What does this intercept tell you about pricing candy bars? Would you buy a candy bar from the vending machine in the hallway if the price is as indicated. Price Yes or No 50 75 1.00 1.25 1.50 1.75 2.00
Employee Turnover The percentage of employees who cease their employment during a year is referred to as employee turnover, and it is a serious issue for businesses. The following table shows the cost, in millions of dollars, to Walmart for a given employee turnover percentage in a year.13 E = employee turnover 10 20 30 40 C = cost 250 400 550 700 a. Show that the data can be modeled by a linear function. b. Find the slope of the linear function. c. Find a linear model for the data. d. Use the result from part c to find the cost to Walmart if employee turnover is 33 in a year.
Femur Length and Height Anthropologists use a linear model that relates femur length to height. The model allows an anthropologist to determine the height of an individual when only a partial skeleton (including the femur) is found. In this problem we find the model by analyzing the data on femur length and height for the eight males given in the table. (a) Make a scatter plot of the data. (b) Find and graph a linear function that models the data. (c) An anthropologist finds a femur of length 58 cm. How tall was the person?
Femur Length and Height Anthropologists use a linear model that relates femur length to height. The model allows an anthropologist to determine the height of an individual when only a partial skeleton including the femur is found. In this problem we find the model by analyzing the data on femur length and height for the eight males given in the table. a Make a scatter plot of the data. b Find and graph a linear function that models the data. c An anthropologist finds a femur of length 58 cm. How tall was the person? Femur length cm Height cm 50.1 178.5 48.3 173.6 45.2 164.8 44.7 163.7 44.5 168.3 42.7 165.0 39.5 155.4 38.0 155.8