Hermann Ebbinghaus (1850–1909) pioneered the study of memory. A 2011 article in the Journal of Mathematical Psychology presents the mathematical model R(t) = a + b(1 + ct)−? for the Ebbinghaus forgetting curve, where R(t) is the fraction of memory retained t days after learning a task; a, b, and c are experimentally determined constants between 0 and

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.EA: Extended Application Using Extrapolation To Predict Life Expectancy

Problem 5EA

See similar textbooks

Similar questions

Because of high tuition costs at state and private universities, enrollments atcommunity colleges have increased dramatically in recent years. The following data show theenrollment (in thousands) for Jefferson Community College from 2001–2009:Year Period (t) Enrollment (1000s)2001 1 6.52002 2 8.12003 3 8.42004 4 10.22005 5 12.52006 6 13.32007 7 13.72008 8 17.22009 9 18.1Compute F10: the Forecast for 2010. Compute Pearson’s Correlation Coefficient Use the Method of Least Squares to obtain the Best-Fit-Line for this data. Use the line to compute the forecast.
National Debt The size of the total debt owed by the UnitedStates federal government continues to grow. In fact,according to the Department of the Treasury, the debt perperson living in the United States is approximately $53,000(or over $140,000 per U.S. household). The following datarepresent the U.S. debt for the years 2001–2014. Since thedebt D depends on the year y, and each input correspondsto exactly one output, the debt is a function of the year. SoD1y2 represents the debt for each year y. Source: www.treasurydirect.govDebt (billions Debt (billionsYear of dollars) Year of dollars)2001 5807 2008 10,0252002 6228 2009 11,9102003 6783 2010 13,5622004 7379 2011 14,7902005 7933 2012 16,0662006 8507 2013 16,7382007 9008 2014 17,824 (a) Plot the points 12001, 58072, 12002, 62282, and so on ina Cartesian plane.(b) Draw a line segment from the point 12001, 58072 to12006, 85072. What does the slope of this line segmentrepresent?(c) Find the average rate of change of the debt from 2002…
Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10-1. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5 on page 493. Manatees Use the listed boat/manatee data. In a year not included in the data below, there were 970,000 registered pleasure boats in Florida. Find the best predicted number of manatee fatalities resulting from encounters with boats. Is the result reasonably close to 79, which was the actual number of manatee fatalities?
Listed below are the numbers of deaths resulting from motor vehicle crashes. Let x represent the year, with 1975 coded as x = 1, 1980 coded as x = 6, 1985 coded as x = 11, and so on. Construct a scatterplot and identify the mathematical model that best fits the given data. Use the best model to find the projected number of deaths for the year 2028. x (year) 1975 1980 1985 1990 1995 2000 2005 2010 D y (deaths) 44,533 51,122 43,809 44,590 41,798 41,960 43,436 32,697 (...) Choose the correct graph below. O A. O B. O C. D. 52000- 52000- 52000- 52000- DDDD 00 X X X X 32000+ 32000 32000+ 32000+ 0 40 0 40 0 40 0 40 What is the equation of the best model? Select the correct choice below and fill in the answer boxes to complete your choice. Enter only nonzero values. (Type integers or decimals rounded to three decimal places as needed.) O A. y= X B. y = + In x O C. y = + O D. X y=² O E. y = x² + X + Use the best model to find the projected number of such deaths for the year 2028. The projected…
Suppose you would like to test the hypothesis that one year of attending a university is worth one years of attending a two-year school (junior college), in terms of effect on wages, using the following econometric model: Y = Bo + B₁X₁ + B2X2 + B3X3 + U where Y = monthly wage in dollars X₁ = number of years attending a two-year college X₂ = number of years at a four-year college X3 = months in the workforce. u = error term The relevant null hypothesis in this case would be Hỏ: B₁-B₂. Equivalently, by creating a new parameter that is a linear combination of ß₁ and B2, this null can be stated as Ho:-
Example 7.12: The following forecasting equation has been derived by a least-squares method: ŷ =10.27 + 1.65x (Base year:1992; x = years; y = tonnes/year) Rewrite the equation by (a) shifting the origin to 1997. (b) expressing x units in months, retaining yn tonnes/year. (c) expressing x units in months and y in tonnes/month.
EXAMPLE 6.56 If λ = 2 per hour and u = 4 per hour in a 2-capacity single- server queueing system, find the effective arrival rate.
Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
A neuroscientist wants to know if physical exercise changes reaction speed in elderly people. A total of 14 older volunteer participants were found. One sample of n = 7 subjects received an exercise treatment, while the second sample (n = 7) of participants were given stretching lessons for the same amount of time per week. Reaction speed was tested on a computer program after six weeks of treatment. Reaction speed was measured in milliseconds. Data shown below. What is the type of statistical test you could use on these data? _____________________ Why this test? ___________________________________________________________ What is the I.V.? ___________________ What is the D.V.? ______________________ Use the data below to fill in the blanks to compute your tcalculated. stretch group exercise group nstretch = ____ dfstretch = _____ nexercise…
A study is made for a particular allergy medication in order to determine the length of relief it provides Y (in hours) in relation to the dosage of medication X (in mg). For this reason, ten patients were given different doses of the medication and were asked to report back when the medication seemed to wear off. Patient #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 Dosage (x) Relief Hours (y) 3 3.5 4 5 6 6.5 7 8 8.5 9 9.1 5.5 12.3 9.2 14.2 16.8 22.0 18.3 24.5 22.7 (i) Draw a scatter diagram. (ii) Calculate the product moment correlation coefficient and comment on your answer. (iii) Construct the least squares regression line.
lecture(12.11D): Researchers were interested in the effects of co-sleeping on nightime waking and crying in infants. .They assesed the number of minutes parents reported that their infants were awake and crying for a period of three days. Five of the infants co-slept with thier mothers(Co) and four infants slept in crib(Cr).The researchers wanted to see if there was a difference in the total number of minutes of crying during the 3 nights. for the two groups. A summary of the data is given below Co-sleepers night time crying in minutes: 8, 4, 7, 7, 6 Crib-sleepers night time crying in minutes: 30, 17, 22, 25 Test the hypotheses at (aplha=.05) level of signifcance. using the 5 step hypotheses testing procedure. Clealy state the null and alternative hypotheses. Round your answer to 2 decimal places.
Question #34 The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 9% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. Assuming his suspicion that 9% of his customers buy a magazine is correct, what is the probability that exactly 6 out of the first 10 customers buy a magazine? 0.0000367300 0.0000674675 0.0000234680 0.0000814185 0.0000341752 0.0000765314