Work these exercises.
Stock Prices The opening price of a stock typically differs somewhat from the closing price the previous day. The accompanying graph shows the stock price
a.
b.
c.
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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_forwardFlood 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_forwardTotal Cost The background for this exercise can be found in Exercises 13 and 14 in Section 3.2. The following table gives the total cost C, in dollars, for a widget manufacturer as a function of the number N of widgets produced during a month. Number N Total cost C 200 7900 250 9650 300 11, 400 350 13, 150 a. What are the fixed costs and variable cost for this manufacturer? b. The manufacturer wants to reduce the fixed costs so that the total cost at a monthly production level of 350 will be 12, 975. What will the new fixed costs be? c. Instead of reducing the fixed costs as in part b, the manufacturer wants to reduce the variable cost so that the total cost at a monthly production level of 350 will be 12, 975. What will the new variable cost be?arrow_forward
- Finding hotel rates A 300-room hotel is two-thirds filled when the nightly room rate is 90. Experience has shown that each 5 increase in cost results in 10 fewer occupied rooms. Find the nightly rate that will maximize income.arrow_forwardFinding mass transit fares The Municipal Transit Authority serves 150,000 commuters daily when the fare is 1.80. Market research has determined that every penny decrease in the fare will result in 1000 new riders. What fare will maximize revenue?arrow_forward
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