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A new fish species is introduced into a lake. Assuming that the population of fish quadruples in the first year, the fish population can be modelled by the logistic curve 10000 P(t): t≥0 1+49e¹ -1.451 where P(t) is the fish population in t years. (a) How many fish were initially introduced into the lake? (b) What is the fish population after 4 years? (c) At what rate is the fish population growing 6 years after introduction? (d) Using the original function, determine the eventual population of fish in the lake (after a long period of time).

A new fish species is introduced into a lake. Assuming that the population of fish quadruples in the first year, the fish population can be modelled by the logistic curve 10000 P(t): t≥0 1+49e¹ -1.451 where P(t) is the fish population in t years. (a) How many fish were initially introduced into the lake? (b) What is the fish population after 4 years? (c) At what rate is the fish population growing 6 years after introduction? (d) Using the original function, determine the eventual population of fish in the lake (after a long period of time).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 33EQ
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A new fish species is introduced into a lake. Assuming that the population of fish quadruples in the first year, the fish population can be modelled by the logistic curve P(t) = 10000 1+49e-1.45t t≥0 where P(t) is the fish population in t years. (a) How many fish were initially introduced into the lake? (b) What is the fish population after 4 years? (c) At what rate is the fish population growing 6 years after introduction? (d) Using the original function, determine the eventual population of fish in the lake (after a long period of time).
Transcribed Image Text:A new fish species is introduced into a lake. Assuming that the population of fish quadruples in the first year, the fish population can be modelled by the logistic curve P(t) = 10000 1+49e-1.45t t≥0 where P(t) is the fish population in t years. (a) How many fish were initially introduced into the lake? (b) What is the fish population after 4 years? (c) At what rate is the fish population growing 6 years after introduction? (d) Using the original function, determine the eventual population of fish in the lake (after a long period of time).
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