The following table gives the total number of U.S adults with diabetes for selected years from 2010 and projected to 2050.Year2010Number (millions)32.3201537.32020202550.059.5203068.3203576.284.191.7204020452050100.0a. Find the logistic function that models these data. Use x equal to the number of years past 2000 and report your model with coefficients rounded to threedecimals places.Logistic function is in the form y =where c =Number, a= NumberNumberand b=1+ae¬bxb. Use the model to predict the number of U.S. adults (in millions) expected to have diabetes in 2042. (Round your answer to one decimal place.)NumbermillionC. According to the model, what is the expected upper limit on the number of U.S. adults (in millions) with diabetes? (Round your answer to one decimalplace.)Numbermilliond. In what year does the model predict that the number of U.S. adults with diabetes will reach 70 million?Number

To Find: a. Find the logistic function that models these data. b. Use the model to predict the…

Answered: The following table gives the total…

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 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...

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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?
What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?
What is the y -intercept on the graph of the logistic model given in the previous exercise?
Recent data suggests that, as of 2013, the rate of growth predicted by Moore’s Law no longer holds. Growth has slowed to a doubling time of approximately three years. Find the new function that takes that longer doubling time into account.
Suppose an investment account is opened with aninitial deposit of 10,500 earning 6.25 interest,compounded continuously. How much will theaccount be warm after 25 years?
The following table gives the total number of U.S adults with diabetes for selected years from 2010 and projected to 2050. Year Number(millions) Year Number(millions) 2010 32.3 2035 76.2 2015 37.3 2040 84.1 2020 50.0 2045 91.7 2025 59.5 2050 100.0 2030 68.3 (a) Find the logistic function that models these data. Use x equal to the number of years past 2000 and report your model with 3 significant digit coefficients. y = 1201+5.25e−0.0637x (b) Use the model to predict the number of U.S. adults (in millions) expected to have diabetes in 2026. (Round your answer to one decimal place.) million adults (c) According to the model, what is the expected upper limit on the number of U.S. adults (in millions) with diabetes? (Round your answer to one decimal place.) million adults (d) In what year does the model predict that the number of U.S. adults with diabetes will reach 80.0 million?
During the start of the COVID 19 pandemic it is assumed that the rate of spread of the corona virus is 18 % daily following a simple logistic growth model by Verhulst. Ten persons are assumed to have acquired the virus in province X. Assuming province X with a population of 2 million does not follow any necessary protocol to prevent the spread of the virus, approximately how many are expected to have acquired the virus after 30 days?
suppose that a population develops according to the logistic equation
A manufacturer of light bulbs finds thatthe mean lifetime of a bulb is 1200 hours. Assume the life of a bulbis exponentially distributed. In a batch of light bulbs, what is the expected time until half the light bulbs in the batch fail?
The analysis of tooth shrinkage byC. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is continuingto decrease and that the evolutionary process has not yetcome to a halt. In northern Europeans, for example, tooth sizereduction now has a rate of 1% per 1000 years. What will be our descendants’ tooth size 20,000 years from now (as a percentage of our present tooth size)?

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