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Drug Epidermic In an epidemiological model used to study the spread of drug use, a single drug user is introduced into a population of N non-users. Under certain assumptions, the number of people expected to use drugs as a result of direct influence from each drug user is given by
Where a, b and k are constants. Find the value of S. Source: Mathematical biology.
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Chapter 8 Solutions
Calculus For The Life Sciences
- The population Pinmillions of Texas from 2001 through 2014 can be approximated by the model P=20.913e0.0184t, where t represents the year, with t=1 corresponding to 2001. According to this model, when will the population reach 32 million?arrow_forwardWorld Population The following table shows world population N, in billions, in the given year. Year 1950 1960 1970 1980 1990 2000 2010 N 2.56 3.04 3.71 4.45 5.29 6.09 6.85 a. Use regression to find a logistic model for world population. b. What r value do these data yield for humans on planet Earth? c. According to the logistic model using these data, what is the carrying capacity of planet Earth for humans? d. According to this model, when will world population reach 90 of carrying capacity? Round to the nearest year. Note: This represents a rather naive analysis of world population.arrow_forwardAltmans z-score Altmans z-score is a financial tool for predicting insolvency in a business. For a certain company, the z-score formula is z=0.84+0.6StockpriceOutstandingsharesTotalliabilty In this exercise, we assume that thre are 45, 000 outstanding shares at a price of 4.80 each. a. Use L, for total liability, in dollard, and give a formula for the z-score for this company. b. Would a larger total liability idicate a better or worese outlook for the company? c. A z-score of 1.81 or lower indicates a high probability of insolvency. What is the smallest value of L that will give a z-score that indicates a high probability on insolvency?arrow_forward
- Market supply The following table shows the quantity S of wheat, in billions of bushels, that wheat supplies are willing to produce in a year and offer for sale at a price P, in dollars per bushel. S = quantity of wheat P = price 1.0 1.35 1.5 2.40 2.0 3.45 2.5 4.50 In economics, it is customary to plot S on the horizontal axis and P on the vertical axis, so we will think of S as a variable and of P as a function of S. a. Show that these data can be modeled by a linear function, and find its formula. b. Make a graph of the linear formula you found in part a. This is called the market supply curve. c. Explain why the market supply curve should be increasing. Hint: Think about what should happen when the price increases. d. How much wheat would suppliers be willing to produce in a year and offer for sale at a price of 3.90 per bushel?arrow_forwardCable TV The following table shows the number C. in millions, of basic subscribers to cable TV in the indicated year These data are from the Statistical Abstract of the United States. Year 1975 1980 1985 1990 1995 2000 C 9.8 17.5 35.4 50.5 60.6 60.6 a. Use regression to find a logistic model for these data. b. By what annual percentage would you expect the number of cable subscribers to grow in the absence of limiting factors? c. The estimated number of subscribers in 2005 was 65.3million. What light does this shed on the model you found in part a?arrow_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
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