Find a logistic function that satisfies the given conditions:initial value = 9, limit to growth = 27, passing through (2, 5)%3D5hpC

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Answered: Find a logistic function that satisfies…

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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Show that for a population that satisfies the logistic model, the maximum rate of growth of population size is rK/4, attained when population size is K/2.
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Your favorite 20 ounce coffee drink from Starbucks contains about 400 mg of caffeine. As soon as you start drinking the coffee, your organs start breaking down the caffeine in your bloodstream and eliminating it from your body. According to Medical News Today, caffeine has a half-life in the body of about 4.5 hours. a) Use the half life of caffeine to find the continuous rate of decay for a function modeling how much caffeine is left in your body t hours after you drink your coffee. Express your answer as a percentage and round your answer to 2 decimal places. The continuous rate of decay for this situation is _____% b) After you drink your coffee, how long will it be until the amount of caffeine in your bloodstream is down to 100 mg? _______hours c) How long will it be until the amount of caffeine in your bloodstream is down below 10 mg? ________hours
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A standard "money demand" function used by macroeconomists has the form In(m) = Bo + B, In(GDP) + B2R, Where m is the quantity of (real) money, GDP is the value of (real) gross domestic product, and R is the value of the nominal interest rate measured in percent per year. Supposed that B, = 2.15 and B, = -0.06. %3D What is the expected change in m if GDP increases by 3%? The value of m is expected to V by approximately%. (Round your response to the nearest integer) What is the expected change in m if the interest rate increases from 1% to 9%? The value of m is expected to ▼ by approximately %. (Round your response to the nearest integer)
A tree farm starts with ten trees. Tree growth is expected to follow logistic growth with a first-order growth rate constant of r = 0.16 yr ' to a maximum of 8,000 trees. Write the equation that relates the number of trees (N) to time (1). What are the values of No, r, and K? Plot the number of trees over time if no harvesting occurs. Go out to about 70 years. What is the maximum sustainable yield (MSY)? How long should you wait before harvesting at the MSY? Determine the standing crop. (The standing crop is the number of trees at steady state when harvesting at the MSY.)
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Find a logistic function that satisfies the given conditions: initial value = 9, limit to growth = 27, passing through (2, 5) %3D