Please help is due thursday A population of bacteria is initially N0 and grows a

Question

Please help is due thursday A population of bacteria is initially N0 and grows at aconstant rate R0. Suppose hours later the bacteria is putinto a different culture such that it now grows at the constantrate R1. Determine the population of bacteria for all thetime. Please help is due thursday A population of bacteria is initially N0 and grows at aconstant rate R0. Suppose hours later the bacteria is putinto a different culture such that it now grows at the constantrate R1. Determine the population of bacteria for all thetime.

Explanation / Answer

QuestionDetails: Please help is due thursday A population of bacteria is initially N0 and grows at aconstant rate R0. Suppose hours later the bacteria
is put into a different culture such that it now grows at theconstant rate R1. Determine the population of
bacteria for all the time.

LET T INDICATE THE TIME IN HOURS FROM THE START AND N THE
POPULATION OF BACTERIA AT THAT TIME.
WE HAVE 2 PHASES
1. PHASE 1
0<=T<=T1, WHEN RATE OF GROWTH =
DN/DT = R0
INTEGRATING
N=R0T+K
AT T=0 , N=N0...SO
N0=0+K....K=N0
HENCE DURING THIS PHASE POPULATION OF BACTERIA =
N= R0T+N0...........................1
PHASE 2
T>=T1
WHEN RATE OF GROWTH =
DN/DT=R1
INTEGRATING
N=R1T+C
AT T=........................N=R0+N0...FROM EQN.1
R0+N0=R1+C
C=R0+N0-R1
HENCE WE GET
N=R1T+R0+N0-R1 =R1T+(R0-R1)+N0..................................2
EQNS. 1 FOR T<= AND EQN.2 FOR T>= WILL GIVE THEPOPULATION OF BACTERIA N
AT ANY TIME T

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