The survival of ancient manuscripts can be modeled by a logistic equation. The number of copies of a particular manuscript was found to approach a limiting value over the five centuries after its publication. LetG(t) represent the proportion of manuscripts known to exist after t centuries out of the limiting value, so that m= 1. For this manuscript, it was found that k=3.4 and Go = 0.00365. Complete parts a through e.C d. Find the proportion of manuscripts and rate of growth after 3 centuries.The proportion of manuscripts after 3 centuries is(Type an integer or decimal rounded to four decimal places as needed.)The rate of growth after 3 centuries is per century.(Type an integer or decimal rounded to four decimal places as needed.)e. What happens to the rate of growth over time?At first, the rate of growthHowever, over time, the rate of growth appears to be▼because the values ofas t increases.

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Answered: proportion of manuscripts and rate of…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter5: Exponential And Logarithmic Functions

Section5.CR: Chapter Review

Problem 18E

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Similar questions

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What might a scatterplot of data points look like if it were best described by a logarithmic model?
An investment account was opened with aninitial deposit of 9,600 and earns 7.4 interest,compounded continuously. How much will theaccount be worth after 15 years?
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?
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What is the carrying capacity for a population modeled by the logistic equation P(t)=250,0001+499e0.45t ? initial population for the model?
Use a graphing calculator to solve each problem. In Example 4, suppose that a birth control program changed the formula for poulation growth to Pt=1000e0.01t. How long will the food supply be adequate? EXAMPLE 4 Using a Graphing Calculator to Solve a popuiation Problem Suppose that a country with a population of 1000 people is growing exponentially according to the population function Pt=1000e0.02t Where t in years. Furthermore, assume that the food supply, measured in adequate food per day per person, is growing linearly according to the function fx=30.625x+2000 In how many years will the population outstrip the food supply?
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