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TEST YOUR UNDERSTANDING | FOR EXAMPLE 5.12
Find a formula for the roof line in the example if the center height is
EXAMPLE 5.12 ROOF LINES
The outside wall of a house is
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Using Models the given model given to answer the question about the object or process being modeled. Arizonans use an average of 40 gal of water per person each day. The number of gallons W of water used by x Arizonans each day is modeled W=40x . (a) Make a table that gives the number of gallons of water used for each 1000-person change in population, from 0 to 5000. (b) What is the population of an Arizona town whose water usage is |20,000 gal per day?arrow_forwardSimple and Compound Interest You have two options for investing $500. The first earns 7% interest compounded annually, and the second earns 7% simple interest. The figure shows the growth of each investment over a 30-year period. (a) Determine which graph represents each type of investment. Explain your reasoning. (b) Verify your answer in part (a) by finding the equations that model the investment growth and by graphing the models. (c) Which option would you choose? Explain.arrow_forwardReminderRound all answers to two decimal places unless otherwise indicated. Skirt LengthOne authors analyzed skirt lengths in the United Kingdom UK and Germany. To get a standardized measure of skirt length, she calculated the ratio. LengthfromshouldertoskirthemLengthfromshouldertoankle The article includes the following graph of the ratio for skirt length in terms of the year. In the graph, the solid line is the ratio in the UK, and the dashed line is the ratio in Germany. FIGURE 1.32 Ratio for skirt length a.Does a larger ratio indicate a longer or a shorter skirt? b.When were skirt lengths shortest in the UK? c.In this period, did skirt lengths in either Germany or the UK ever reach to the ankle?arrow_forward
- Reminder Round all answers to two decimals places unless otherwise indicated. An Overflow Pipeline An overflow pipeline for a pond is to run in a straight line from the pond at maximum water level a distance of 96 horizontal feet to a drainage area that is 5 vertical feet below the maximum water level see Figure 3.21. How much lower is the pipe at the end of each 12-foot horizontal stretch?arrow_forwardUsing Models the given model given to answer the question about the object or process being modeled. A mountain climber models the temperature T (in F ) at elevation h (in ft.) by T=700.003h (a) Find the temperature at an elevation of 1500 ft. (b) If the temperature is 64F , what is the elevation.arrow_forwardBiology The metabolic rate of an ectothermic organism increases with increasing temperature within a certain range. Experimental data for the oxygen consumption C (in microliters per gram per hour) of a beetle at certain temperatures can be approximated by the model C=0.45x21.65x+50.75,10x25 where x is the air temperature in degrees Celsius. a The oxygen consumption is 150 microliters per gram per hour. What is the air temperature ? b When the air temperature increases from 10C to 20C, the oxygen consumption increases by approximately what factor ?arrow_forward
- Reminder Round all answers to two decimals places unless otherwise indicated. A Wheelchair Service Ramp The Americans with Disabilities Act ADA requires, among other things, that wheelchair service ramps have a slope not exceeding 1/12. a. Suppose the front steps of a building are 2 feet high. You want to make a ramp conforming to ADA standards that reaches from the ground to the top of the steps. How far away from the building is the base of the ramp? b. Another way to give specifications on a ramp is to give allowable inches of rise per foot of run. In these terms, how many inches of rise does the ADA requirement allow in 1 foot of run?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Gravity on Earth and on MarsThe acceleration due to gravity near the surface of a planet depends on the mass of the planet; larger planets impart greater acceleration than smaller ones. Mars is much smaller than Earth. A rock is dropped from the top of a cliff on each planet. Give its location as the distance down from the top of the cliff. a.On the same coordinate axes, make a graph of distance down for each of the rocks. b.On the same coordinate axes, make a graph of velocity for each of the rocks.arrow_forwardTEST YOUR UNDERSTANDINGFOR EXAMPLE 5.15 What range of lumber volume is available for a 10-foot-long log? EXAMPLE 5.15LUMBER FROM LOGS The Scribner rule for estimating the amount of lumber that can be obtained from a log is V=L16(0.79D22D4). Here V is the volume, in board feet, L is the length of the log, in feet, and D is the diameter of the smaller end of the log, in inches. We consider logs of length 16feet. The Scribner rule is used for logs whose diameters range from 6 to 28 inches.arrow_forward
- Reminder Round all answer to two decimal places unless otherwise indicated. Gasoline Prices In 1960, the average price per gallon of gasoline was 31 cents per gallon. Form 1960 to 2000, prices increased, on average, by 2.5 cents per gallon per year. 4 a. Using G for the price, in cents per gallon, and t for the time, in years, since 1960, use a formula to express G as linear function of t. b. What price per gallon does the model yield for 1990? Note: The actual price was 1.00 per gallon. c. Use the Internet to find the average price of gasoline for the current year. Does the model from part a give a price near the current price?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_forwardReminder Round all answer to two decimal places unless otherwise indicated. Hair Growth When you are 18 years old you have a hair that is 14 centimeters long, and your hair grows about 12 centimeters each year. Let H(t) be the length, in centimeters, of that hair t years after age 18. a. Find a formula that gives H as a linear function of t. b. How long will it take for the hair to reach a length of 90 centimeters?arrow_forward
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