Sam was 28 inches tall on her first birthday, 50 inches tall on her 8th,and 62 inches tall on her 14th.(a) CAS) Let t represent Sam's age in years, and let h represent herheight in inches. Determine the values of M, A, and k for a logistic model,1+ Ae-kt that fits the given height data.(b) What is Sam's theoretical long-term expected height? That is, what islim h(t)?h(t) =(c) At what age does the model predict that Sam will reach 95% of herexpected maximum height?

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Answered: Sam was 28 inches tall on her first…

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 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 is the y -intercept on the graph of the logistic model given in the previous exercise?
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.
Sam was 28 inches tall on her first birthday, 50 inches tall on her 8th, and 62 inches tall on her 14th. (a) Let t represent Sam's age in years, and let h represent her height in inches. Determine the values of M, A, and k for a logistic model, h(t) = M / ( 1+ Ae-kt) , that fits the given height data. (b) What is Sam's theoretical long-term expected height? That is, what is limt➔∞h(t)? (c) At what age does the model predict that Sam will reach 95% of her expected maximum height?
Suppose a new magazine initially sells 600 copies per month. Research indicates that a vigorous advertising campaign could increase sales by 40% each month if our market were unlimited. But research also indicates that magazine sales in our area are unlikely to exceed 2400 per month. Make a logistic model of projected magazine sales. a) N = 600 / 1+3e^-0.336t b) N = 2400 / 1+3e^-0.336t c) N = 40 / 1+3e^-0.336t d) N = 2400 / 1+40e^-0.336t
Compute the forecasted values for Yt for July and August in 2020 by using the modelsstated in (c) and (d)
For the 23 space shuttle flights before the Challenger mission disaster in 1986, The following table shows the temperature (◦F) at the time of the flight and whether at least one primary O-ring suffered thermal distress. Use logistic regression to model the effect of temperature on the probability of thermal distress. Interpret the effect. Estimate the probability of thermal distress at 31◦F, the temperature at the time of the Challenger flight. At what temperature does the estimated probability equal 0.50? At that temperature, give a linear approximation for the change in the estimated probability per degree increase in temperature. Interpret the effect of temperature on the odds of thermal distress. Test the hypothesis that temperature has no effect, using (i) the Wald test, (ii) the likelihood-ratio test.

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