Stimulus-response One of the early results in psychology relating the magnitude of a stimulus x to the magnitude of a response y is expressed by the equation
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- Population Statistics The table shows the life expectancies of a child (at birth) in the United States for selected years from 1940 through 2010. A model for the life expectancy during this period is y=63.6+0.97t1+0.01t,0t70 Where y represents the life expectancy and t is the time in years, with t = 0 corresponding to 1940. (a) Use a graphing utility to graph the data from the table and the model in the same viewing window. How well does the model fit the data? Explain. (b) Determine the life expectancy in 1990 both graphically and algebraically. (c) Use the graph to determine the year when life expectancy was approximately 70.1. verify your answer algebraically. (d) Find the y-intercept of the graph of the model. What does it represent in the context of the problem? (e) Do you think this model can be used to predict the life expectancy of a child 50 years from now?arrow_forwardEarthquake the graph shows the vertical acceleration of the Ground from the 1994 Northridge earthquake in Los Angles, as measured by a seismograph. (Here t represents the time in seconds.) (a) At what time t did the earthquake first make noticeable movement of the Earth? (b) At what time t did the earthquakes seem to end? (c) At what time t was the maximum intensity of the earthquake list reachedarrow_forwardStopping distance, The stopping distance of an automobile is the distance travelled during the driver’s reaction time plus the distance travelled after the driver applies the brakes. In an experiment, researchers measured these distances (in feet) when the automobile was traveling at a speed of x. miles per hour on dry, level pavement, as shown in the bar graph. The distance travelled during the reaction time R was R=1.1x and the braking distance B was B=0.0475x20.001x+0.23. (a) Determine the polynomial that represents the total stopping distance T. (b) Use the result of part (a) to estimate the total stopping distance when x=30,x=40, andx=55 miles per hour. (c) Use the bar graph to make a statement about the total stopping distance required forincreasing speeds.arrow_forward
- Population Statistics The table shows the life expectancies of a child (at birth) in the United States for selected years from 1940 through 2010. A model for the life expectancy during this period is y=63.6+0.97t1+0.01t,0r70 Where y represents the life expectancy and t is the time in years, with t=0 corresponding to 1940. (a) Use a graphing utility to graph the data from the table and the model in the same viewing window. How well does the model fit the data? Explain (b) Determine the life expectancy in 1990 both graphically and algebraically. (c) Use the graph to determine the year when life expectancy was approximately 70.1. Verify your answer algebraically. (d) Identify the y-intercept of the graph of the model. What does it represent in the context of the problem? (e) Do you think this model can be used to predict the life expectancy of a child 50 years from now? Explainarrow_forwardMonthly Payment for a Home: If you borrow 120,000 at an APR of 6 in order to buy a home, and if the lending institution compounds interest continuously, then your monthly payment M=M(Y), in dollars, depends on the number of years Y you take to pay off the loan. The relationship is given by M=120,000(e0.0051)1e0.06Y. a. Make a graph of M versus Y. in choosing a graphing window, you should note that a home mortgage rarely extends beyond 30 years. b. Express in functional notation your monthly payment if you pay off the loan in 20 years, and then use the graph to find that value. c. Use the graph to find your monthly payment if you pay off the loan in 30 years. d. From part b to part c of this exercise, you increased the debt period by 50. Did this decrease your monthly payment by 50? e. Is the graph concave up or concave down? Explain your answer in practical terms. f. Calculate the average decreases per year in your monthly payment from a loan period of 25 to a loan period of 30 years.arrow_forwardPopulation The population y (in thousands) of Raleigh, North Carolina, from 2000 to 2014 can be approximated by the model y=11.09t+293.4,0t14, where t represents the year, with t=0 corresponding to 2000 (see figure). (a) Graphically estimate the y-intercept of the graph. (b) Find algebraically and interpret the y-intercept of the graph. (c) Use the model to predict the year in which the population will be 538,000. Does your answer seem reasonable? Explain.arrow_forward
- Flood Control A river is 8 feet above its flood stage. The water is receding at a rate of 3 inches per hour. Write a mathematical model that shows the number of feet above flood stage after t hours. Assuming the water continually recedes at this rate, when will the river be 1 foot above its flood stage?arrow_forwardA Cup of Cofee The temperature C of a fresh cup of coffee t minutes after it is poured is given by C = 125e-0.03t 75 degree Fahrenheit. a. Make a graph of Cversus t. b. The coffee is cool enough to drink when its temperature if 150 degrees. When will the coffee be cool enough to drink? c. What is the temperature of the coffee in the pot? Note :We are assuming that the coffee pot is being kept hot and its the same temperature as the cup of coffee when it was poured. d.What is the temperature in the room where you are drinking the coffee? Hint: If the coffee is left to cool a long time, it will reach room temperature.arrow_forwardDepreciation A hospital purchases a new magnetic resonance imaging (MRI) machine for $1.2 million. The depreciated value y (reduced value) after t years is given by y=1,200,00080,000t,0t10. Sketch the graph of the equation.arrow_forward
- World Crude Oil Production In 1956, M.King Hubbert proposed a model to analyse crude oil production. His model, with updated data, gives world crude oil production as P=254.43e0.042t(1+2.12e0.042t)2 Here P is measured in billions of barrels per year, and t is time, in year, since 2000. a.Make a graph of world crude oil production for 2000 through 2040. b.When does this model predict a peak in world crude oil production? c.What is the maximum crude oil production predicted by this model?arrow_forwardBuilders Old Measurement The Builders Old Measurement was instituted by law in England in 1773 as the way to estimate the total tonnage T of a wooden ship from its beam width W and length L, both measured in feet. The formula is T=(L0.6W)W2188 In this exercise, we consider wooden ships of length 150 feet. a.Make a graph of T versus W, including beam widths up to 250 feet. b. What is the maximum tonnage for a ship of this length? c.Comment on the dimensions of the ship from part b. d. What is the maximum tonnage of a ship whose width is no more than half its length? That is, we assume that the beam width is at most 75 feet.arrow_forward
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