The following table shows the total spent on research and development by industry in a country, in billions of dollars, for the period 2002-2012.Year t(years since 2000)Spending ($ billion) 194 197Find the logarithmic regression model of the form S(t)- A In(t) + C with coefficients A and C rounded to two decimal places.s(t)-234567197 207 218 2298237910 11 12224 222 234 245

We have given data about the research and development industry spent amount in a country for period…

Answered: The following table shows the total…

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.1: Logistic Functions

Problem 13E

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Table 2 shows a recent graduate’s credit card balance each month after graduation. a. Use exponential regression to fit a model to these data. b. If spending continues at this rate, what will the graduate’s credit card debt be one year after graduating?
Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?
World 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.
Cable 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?
The US. import of wine (in hectoliters) for several years is given in Table 5. Determine whether the trend appearslinear. Ifso, and assuming the trend continues, in what year will imports exceed 12,000 hectoliters?
Life Expectancy The following table shows the average life expectancy, in years, of a child born in the given year42 Life expectancy 2005 77.6 2007 78.1 2009 78.5 2011 78.7 2013 78.8 a. Find the equation of the regression line, and explain the meaning of its slope. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 2019? e. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 1580?2300
The fox population in a certain region has an annualgrowth rate of 9 per year. In the year 2012, therewere 23,900 fox counted in the area. What is the foxpopulation predicted to be in the year 2020 ?
a scuba diver used her camera equipment to measure the intensity of light, in lux, as she dove into the lake. She compared her readings with the depth of water at each point. light intensity(lux) - 5.0, 4.0, 3.0, 2.0, 1.0 depth of water(m) - 2.3, 3.1, 4.0, 5.4, 7.7 (a) use logarithmic regression to model data, round all values to the nearest hundredth (b) At what depth, to the nearest tenth of a metre is the light intensity 3.6 lux (c) What is the light intensity at the surface, round to the nearest tenth
Nitrogen dioxide, NO₂, is an air pollutant resulting from burning fossil fuels in cars and power plants. The following table shows the decrease in the national average of the concentration in parts per billion (ppb) of NO₂ for selected years. Year 2014 40.8107 2015 2016 2017 2018 39.7886 38.7972 37.8209 36.8752 NO₂ (ppb) Use exponential regression to find an exponential decay function for the concentration, C, of NO₂ t years after 2014. Round constants to the nearest ten-thousandth. c-40.8114 (0.9750) Use the model to predict the concentration of NO₂ (in ppb) in 2045. Round to the nearest whole number. 21 x ppb
Nitrogen dioxide, NO2, is an air pollutant resulting from burning fossil fuels in cars and power plants. The following table shows the decrease in the national average of the concentration in parts per billion (ppb) of NO2 for selected years. Year 2014 2015 2016 2017 2018 NO2 (ppb) 40.8107 39.7886 38.7972 37.8209 36.8752 Use exponential regression to find an exponential decay function for the concentration, C, of NO2 t years after 2014. Round constants to the nearest ten-thousandth. C = Use the model to predict the concentration of NO2 (in ppb) in 2050. Round to the nearest whole number. ? ppb
The table to the right shows the number of internet hosts from 1994 to 2012. (A) Let x represent the number of years since 1994 and find an exponential regression model y=abx for the number of internet hosts. (B) Use the model to estimate the number of internet hosts in 2022. Internet Hosts (millions) Year Hosts 1994 2.6 1997 15 2000 73.5 2003 184.1 2006 432.3 2009 666.4 2012 910.7
The table shows the number of internet users worldwide since 1994. (A) Let x represent the number of years since 1994 and find an exponential regression model (y ab*) for this data set (B) Use the model to estimate the number of hosts in 2022 (to the nearest million). (A) Write the regression equation yab -0-0 (Round to four decimal places as needed.) Year 1994 1997 2000 2003 2006 2009 2012 Internet Users (millions) Users 24 17.4 68.8 173.5 412.8 656.5 824.3

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