1. The following data represent the growth of a bacteria population over time.Number of Hours07Number of Bacteria8502250124500204213 500 287 200a) Create both a graphical model and an algebraic model for the data.b) Determine the length of time it took for the population to double. [5]

The growth of the bacteria is typically modelled using the exponential growth formula.Let P(t) be…

Answered: 1. The following data represent the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Pesticide danger: One of the factors that determines the degree of risk a pesticide poses to human health is the rate at which a pesticide is absorbed into skin after contact. An important question is whether the amount in the skin continues to increase with the length of the contact, or whether it increases for only a short time before leveling off. To investigate this, measured amounts of a certain pesticide were applied to 20 samples of rat skin. Four skins were analyzed at each of the time intervals 1, 2, 4, 10, and 24 hours. The amounts of the chemical (in micrograms) that were in the skin are given in the following table.
A student is trying to determine the doubling time for a population of the bacterium Giardia lamblia (G. lamblia). He starts a culture in a nutrient solution and counts the bacteria every 4 hours. His data are shown in the table. Time (h) 0 4 8 12 16 20 24 Bacteria count (CFU/mL) 37 47 63 78 105 130 176 (a) Make a scatter plot of the data. (b) Use a calculator to find an exponential curve f(x) = b · ax that models the bacteria population x hours later. (Round your answer to three decimal places.) f(x) = (c) Graph the model from part (b) together with the scatter plot in part (a). Use the feature to determine how long it takes for the bacteria count to double. (Round your answer to one decimal place.) h
(Medicare). The annual expenditures for Medicare (in billions of dollars) by the US Government for selected years since 1980 are shown in Table 4. Let x represent the years since 1980. (Use 4 decimal places in all answers.) Table 4: Medicare Expenditures Year Billion $ 1980 37 1985 72 1990 111 1995 181 2000 197 2005 330 A. Find the exponential regression model for the data.M(x) = B. What is the r2 value for this model?r2 = C. Extimate (to the nearest billion) the expenditures in 2008?The Medicare expenditures in 2008 were about $ billion.
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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…
Pesticide danger: One of the factors that determines the degree of risk a pesticide poses to human health is the rate at which a pesticide is absorbed into skin after contact. An important question is whether the amount in the skin continues to increase with the length of the contact, or whether it increases for only a short time before leveling off. To investigate this, measured amounts of a certain pesticide were applied to 20 samples of rat skin. Four skins were analyzed at each of the time intervals 1, 2, 4, 10, and 24 hours. The amounts of the chemical (in micrograms) that were in the skin are given in the following table. Duration Amounts Absorbed 1 1.5 2.7 1.6 1.6 2 1.7 1.7 2.4 2.3 4 1.4 2.1 1.6 1.2 10 2.4 1.2 2.1 2.6 24 2.2 1.8 1.7 1.3 Send data to Excel Part: 0 / 2 Part 1 of 2 (a) Construct an ANOVA table. Round your answers to four decimal places. One-way ANOVA: Pesticide Amount Source DF SS MS F Duration Error Total
Consider the following table that gives the population of City A from Year 1 to Year 6. Complete all parts (a-k) to this question. Part 1: Fill-in the last two columns in the table. List your answers as a - j for the chart and answer the question k below. Round growth rate to the nearest ten-thousandth (4 decimal places). Population of City A, Year 1 to year 6 Year Population (P) Change ΔP{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>P</mi></math>"} Growth Rate ΔPP{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>∆</mo><mi>P</mi></mrow><mi>P</mi></mfrac></math>"} 1 315,422 N/A N/A 2 320,421 a. b. 3 321,765 c. d. 4 322,162 e. f. 5 331,165 g. h. 6 331,200 i. j. Part 2: k. Does it make sense to fit this data with an exponential model? Why or why…

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1. The following data represent the growth of a bacteria population over t Number of Hours 0 7 20 42 Number of Bacteria 850 2250 13 500 287 200 12 4500 a) Create both a graphical model and an algebraic model for the data. b) Determine the length of time it took for the population to double. [5]