The survival of ancient manuscripts can be modeled by the logistic equation. The number of copies of a particular manuscript was found to approach a limiting value over the five centuries after its publication in the year 725. Let G(t)represent the proportion of manuscripts known to exist after t centuries out of the limiting value, so that m= 1. For this manuscript, k = 3.8 and Go = 0.00319.a. Find the growth function G(t) for the proportion of copies of the manuscript found.b. Find the proportion of manuscripts and their rate of growth after 2 centuries.a. G(t)=

The survival of ancient manuscripts can be modeled by the logistic equation. The number of copies of…

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Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Suppose that in a logistic model the percentage growth rate G per year (in decimal form) as a function of N declines from G = 0.12 when N = 0 to G = 0 when N= 366. (a) What is the r value? r = (b) What is the carrying capacity? K = (c) At what value of N will there be a maximum growth rate? N = | Need Help? Read It
If the population of a Nigeria doubles in 9 years, ﬁnd the growth rate k. Assume that the population increases exponentially.
A study of Maryland's portion of Chesapeake Bay found the following information about stocks of market-sized oysters.† In 1994, the stocks were 218 million. (This is the number you will use for the initial population N(0).) The carrying capacity is 5089 million oysters. The intrinsic exponential growth rate is 0.274 per year. (a) Find a logistic model N(t) for the number, in millions, of market-sized oysters. Take t to be the time in years since 1994. (Rround all regression parameters to three decimal places.) N(t) = (b) Plot the graph of the model you found in part (a) over the first 20 years. (c) How many market-sized oysters does your model predict for 2007? Round your answer, in millions, to the nearest whole number. million oysters (d) The actual number of market-sized oysters was found to be 82 million. Use the Internet to find possible explanations for the reduced levels of oysters in Chesapeake Bay.
A population is now 3000 and is growing exponentiallywith a growth constant of .02, what will be the average population be during the next 50 years?
A certain phenomenon has an initial value of 12 and grows at a rate of 8% per year. Give an exponential function N = N(t) that describes this phenomenon. (Use t in years as your variable.)

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