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3. A certain bacterium exponential growth is expressed with the following function: P = P, * ekt where P = total population after time t (gram)

3. A certain bacterium exponential growth is expressed with the following function: P = P, * ekt where P = total population after time t (gram)

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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3. A certain bacterium exponential growth is expressed with the following function: P = Po * ekt where P = total population after time t (gram) Po = Initial population (gram) k = percent rate of growth t = time (day) Variation of the population with time is given in the following table. t (day) 1 3 5 7 9 11 13 15 17 19 P (gram) 0.64 1.06 1.75 2.88 | 4.74 | 7.82 | 12.90 | 21.26 | 35.05 | 57.79 a) Linearize the exponential growth expression and plot the linearized equation by using the given data. b) Calculate initial population (Po) and percent rate of growth (k). c) How much bacteria (P) can we grow in 2 weeks?
Transcribed Image Text:3. A certain bacterium exponential growth is expressed with the following function: P = Po * ekt where P = total population after time t (gram) Po = Initial population (gram) k = percent rate of growth t = time (day) Variation of the population with time is given in the following table. t (day) 1 3 5 7 9 11 13 15 17 19 P (gram) 0.64 1.06 1.75 2.88 | 4.74 | 7.82 | 12.90 | 21.26 | 35.05 | 57.79 a) Linearize the exponential growth expression and plot the linearized equation by using the given data. b) Calculate initial population (Po) and percent rate of growth (k). c) How much bacteria (P) can we grow in 2 weeks?
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