Population Growth Model Development
Research in cell and tissue engineering often involves growing cells in the lab in a dish. Imagine
having a single 120 cm2 dish that has been seeded with 1500 cells/cm2. The dish can only
sustain 9×107 cells. With this seeding of the dish, the maximum that the dish can sustain
(carrying capacity) is reached in about 20-25 days. The growth rate, r, of this cell type is known
to be 0.75 cells per day (ππππ‘β πππ‘π β ππππ‘β πππ‘π).
This cell population follows a logistic population growth model:
ππ(π‘)
ππ‘ = ππ(π‘)(1 β π(π‘)/πΎ ),
where P(t) is the size of the population at time, t, K is a constant corresponding to the
saturation level (carrying capacity) and r > 0 is the birth rate.
1. Write a MATLAB script for the numerical solution of this cell population problem
utilizing the Euler differential equation solver as demonstrated in class.Research in cell and tissue engineering often involves growing cells in the lab in a dish. Imagine
having a single 120 cm2 dish that has been seeded with 1500 cells/cm2. The dish can only
sustain 9×107 cells. With this seeding of the dish, the maximum that the dish can sustain
(carrying capacity) is reached in about 20-25 days. The growth rate, r, of this cell type is known
to be 0.75 cells per day (ππππ‘β πππ‘π β ππππ‘β πππ‘π).
This cell population follows a logistic population growth model:
ππ(π‘)
ππ‘ = ππ(π‘)(1 β π(π‘)/πΎ ),
where P(t) is the size of the population at time, t, K is a constant corresponding to the
saturation level (carrying capacity) and r > 0 is the birth rate.
1. Write a MATLAB script for the numerical solution of this cell population problem
utilizing the Euler differential equation solver as demonstrated in class.Β Research in cell and tissue engineering often involves growing cells in the lab in a dish. Imagine
having a single 120 cm2 dish that has been seeded with 1500 cells/cm2. The dish can only
sustain 9×107 cells. With this seeding of the dish, the maximum that the dish can sustain
(carrying capacity) is reached in about 20-25 days. The growth rate, r, of this cell type is known
to be 0.75 cells per day (ππππ‘β πππ‘π β ππππ‘β πππ‘π).
This cell population follows a logistic population growth model:
ππ(π‘)
ππ‘ = ππ(π‘)(1 β π(π‘)/πΎ ),
where P(t) is the size of the population at time, t, K is a constant corresponding to the
saturation level (carrying capacity) and r > 0 is the birth rate.
1. Write a MATLAB script for the numerical solution of this cell population problem
utilizing the Euler differential equation solver as demonstrated in class.Β matlabΒ MATLAB Answers β New Questions
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