Problem 1 dP dt Consider the population model = 4 P 1 where P(t) is the populati

Question

Problem 1 dP dt Consider the population model = 4 P 1 where P(t) is the population at time t. 20 26 (a) For what values of P is the population in equilibrium? Equilibrium Population Note: If there is more than one solution, separate your answers with commas. (b) For what values of P is the population increasing? Population is Increasing: Note: Use interval notation. (c) For what values of P is the population decreasing? Population is Decreasing: Note: Recall for what values of P population models are defined. Note: You can earn partial credit on this problem.

Explanation / Answer

From the given question,

dP/dt = 4P( 1- P/20)(P/26 -1), where P(t) is population at time t

a) population is in equilibrium if dP/dt=0

4P(1- P/20)(P/26 -1)=0

P=0, ( 1- P/20)=0, (P/26 -1)=0

P=0, P=20, P=26

b) Population is increasing if dP/dt > 0

4P(1- P/20)(P/26 -1)>0

4P(20-P)(P-26)>0

20<P<26

c) Population is decreasing if dP/dt < 0

4P(1- P/20)(P/26 -1)<0

4P(20-P)(P-26)<0

0<P<20, P>26

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