*R2.47. Companies assets and sales How are the assets andsales of major corporations related? The data set is thesame as that for Exercise 2.44. The variable Banks in thedata set is 1 for the banks and 0 for the other companies.As Exercise 2.44 showed, it is best to take the logarithm ofmost of these variables. Here are a scatterplot and a regres-sion relating the logarithm of assets and the logarithm ofsales. The banks are shown in red:LAss4.50-3.753.002.25 3.00 3.75LSIResponse variable is: LogAssetsR squared = 73.7 % s = 0.2741VariableInterceptLogSalesBanksCoefficient0.4225630.8684880.9456754.50a) What is an appropriate interpretation of the coefficient ofLogSales?b) What is an appropriate interpretation of the coefficient ofBanks?c) Is the use of a variable such as Banks appropriate forthese data? Explain.

Answered: Image /qna-images/answer/651da22f-361e-427b-9c6a-5eeddb853fdc.jpg

Answered: *R2.47. Companies assets and sales How…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 2TI: Sales of a video game released in the year 2000 took off at first, but then steadily slowed as time...

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Sales of a video game released in the year 2000 took off at first, but then steadily slowed as time moved on. Table 4 shows the number of games sold, in thousands, from the years 20002010. a. Let x represent time in years starting with x=1 for the year 2000. Let y represent the number of games sold in thousands. Use logarithmic regression to fit a model to these data. b. If games continue to sell at this rate, how many games will sell in 2015? Round to the nearest thousand.
What type (s) of translation (s), if any, affect thedomain ofa logarithmic function?
What type (s) of translation(s), if any, affect the range of a logarithmic function?
Enter the data from Table 2 into a graphing calculator and graph the ranking scatter plot. Determine whetherthe data from the table would likely represent a function that is linear, exponential, or logarithmic.
How the Logarithm IncreasesIf logx=8.3 and logy=10.3, how do x and y compare?
How is the logarithmic function f(x)=logb(x) related to the exponential function g(x)=bx ? Whatis the result of composing these two functions?
Suppose that the initial size of a population is n0 and the population grows exponentially. Let n(t) be the size of the population at time t. (a) Write a formula for n(t) in terms of the doubling time a. (b) Write a formula for n(t) in terms of the relative growth rate r.
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?
Buffalo: Waterton Lakes National Park of Canada, where the Great Plains dramatically meet the Rocky Mountains in Alberta, has a migratory buffalo bison herd that spends falls and winters in the park. The herd is currently managed and so kept small; however, if it were unmanaged and allowed to grow, then the number N of buffalo in the herd could be estimated by the logistic formula N=3151+14e0.23t Here t is the number of years since the beginning of 2002, the first year the herd is unmanaged. a. Make a graph of N versus t covering the next 30 years of the herds existance corresponding to dates up to 2032. b. How many buffalo are in the herd at the beginning of 2002? c. When will the number of buffalo first exceed 300?. d. How many buffalo will there eventually be in the herd? e. When is the graph of N, as a function of t, concave up? When is it concave down? What does this mean in terms of the growth of the buffalo herd?.
Graph the following logistic function, first discussed in Example 5. Use window settings of 0,20 for x and 0,1,500,000 for y. Pt=1,200,0001+1199e-0.4t
Modeling Human Height with a Logistic Function A male child is 21inches long at birth and grows to an adult height of 73inches. In this exercise, we make a logistic model of his height as a function of age. a. Use the given information to find K and b for the logistic model. b. Suppose he reaches 95 of his adult height at age 16. Use this information and that from part a to find r. Suggestion: You will need to use either the crossing-graphs method or some algebra involving the logarithm. c. Make a logistic model for his height H, in inches, as a function of his age t, in years. d. According to the logistic model, at what age is he growing the fastest? e. Is your answer to part d consistent with your knowledge of how humans grow?

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