Concept explainers
TEST YOUR UNDERSTANDING | FOR EXAMPLE
A small dog will weigh
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Find an exponential model for
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Check out a sample textbook solutionChapter 4 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Weight Versus Height The following data show the height h, in inches, and weight w, in pounds, of an average adult male. h 61 62 66 68 70 72 74 75 w 131 133 143 149 155 162 170 175 a Make a power model for weight versus height. b According to the model from part a, what percentage increase in weight can be expected if height is increased by 10?arrow_forwardTEST YOUR UNDERSTANDING | FOR EXAMPLE 4.14 If light arriving from a star is twice the intensity of the light from Vega, what is the magnitude of the star? Caution: Is the relative intensity 2 of 1/2?arrow_forwardTEST YOUR UNDERSTANDING FOR EXAMPLE 3.6 The following table shows hypothetical enrollment E at a college t years after 2012. t = years since 2012 0 1 2 3 4 E = enrollment 8641 8975 9309 9643 9977 Show that the data are linear, and find a linear model for the data.arrow_forward
- TEST YOUR UNDERSTADING FOR EXAMPLE 3.5 A donation to the university is required for the privilege of purchasing premium season football passes. The cost is a linear function of the number of season passes. It costs 8000 to get season passes for myself and my spouse. To get passes for my entire family of 5, it costs 17,000. Use a formula to express the total cost C, in dollars, of n season passes. EXAMPLE 3.5 CHANGING CELSIUS TO FAHRENHEIT Temperature F=F(C) in Fahrenheit is a linear function of the temperature C in Celsius. A lab assistant placed a Fahrenheit thermometer beside a Celsius thermometer and observed the following: When the Celsius thermometer reads 30 degree (C=30), the Fahrenheit thermometer reads 86 degrees (F=86). When the Celsius thermometer reads 40 degrees, the Fahrenheit thermometer reads 104 degrees. Part 1 Use a formula to express F as a linear function of C. Part 2 At sea level, water boils at 212 degrees Fahrenheit. What temperature in degrees Celsius makes water boil? Part 3 Explain in practical terms what the slope means in this setting.arrow_forwardLean Body Weight in Males A persons lean body weight L is the amount that he or she would weigh if all body fat were marginally to disappear. One text 3 gives the equation that practitioners can use most feasibly in the field to predict lean body weight in young males. The equation is L=98.42+1.08W-4.14A Here L is the lean body weight in pounds, W is the weight in pounds and A is the abdominal circumference in inches. Find the approximate lean body weight of a young adult male who weighs 188 pounds and has an abdominal circumference of 35 inches. What is the weight of his body fat? What is his body fat percent?arrow_forwardTEST YOUR UNDERSTANDING The following table shows the average price P, in dollars, of a gallon of regular gas t years after 2000. t = year since 2000 0 2 4 7 8 P = price in dollars 1.51 1.36 1.88 2.80 3.27 Find the equation of the regression line for P as a function of t. What price does your model give for gas in 2009? Compute your answer with the actual value of 2.35.arrow_forward
- Dropping Rocks on Mars The behavior of objects falling near Earths surface depends on the mass of Earth. On Mars, a much smaller planet than Earth, things are different. If Galileo had performed his experiment on Mars, he would have obtained the following table of data. t = seconds V = feet per second 0 0 1 12.16 2 24.32 3 36.48 4 48.64 5 60.8 a. Show that these data can be modeled by a linear function, and find a formula for the function. b. Calculate V10 and explain in practical terms what your answer means. c. Galileo found that the acceleration due to gravity of an object falling near Earths surface was 32 feet per second per second. Physicists normally denote this number by the letter g. If Galileo had lived on Mars, what value would he have found for g?arrow_forwardTEST YOUR UNDERSTANDING | FOR EXAMPLE 4.7 The salinity of a saltwater aquarium is being raised to a target value of 32 parts per thousand of dissolved solids in the tank. The table below shows the difference D between the target salinity and the current salinity S after thours. Both D and S are measured in parts per thousand. t=timeinhours 0 1 2 3 4 D=salinitydifference 32 25.60 20.48 16.38 13.11 Make a model of D as an exponential function of t. Find a formula that gives the salinity S as s function of t.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning