Exercise 0.4 A tumour may be regarded as a population of multiplying cells. It is foundempirically that the "birth rate" 3, of the cells in a tumour decreases exponentially with time,so that 3(t) = Boe-at where a and 3o are positive constants, and hencedPBoe-at P,P(0) = PodtShow thatP(t) = P, exp (1 -e)Show that P(t) cannot grow beyond a certain limit and find this limit.

Given the differential equation is dPdt=β0e-αtP and P0=P0

Exercise 0.4 A tumour may be regarded as a population of multiplying cells. It is found empirically that the "birth rate" 8, of the cells in a tumour decreases exponentially with time, so that 3(t) = Boe af where a and are positive constants, and hence dP = Boe-a P, P(0) = P dt Show that P() = R,esp 1 - c) %3D Show that P(t) cannot grow beyond a certain limit and find this limit.

Exercise 0.4 A tumour may be regarded as a population of multiplying cells. It is found empirically that the "birth rate" 8, of the cells in a tumour decreases exponentially with time, so that 3(t) = Boe af where a and are positive constants, and hence dP = Boe-a P, P(0) = P dt Show that P() = R,esp 1 - c) %3D Show that P(t) cannot grow beyond a certain limit and find this limit.

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Exponential And Logarithmic Functions

Section5.5: Exponential And Logarithmic Models

Problem 30E: The table shows the mid-year populations (in millions) of five countries in 2015 and the projected...

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