According to Malthusian population growth (or decay) model, the population of a body changes at a...

Transcribed Image Text:

According to Malthusian population growth (or decay) model, the population of a body changes at a rate proportional to the population at any time. Thus, if P= P(t) is the population at time t, then P' = aP where a is a positive constant. In this exercise, you will verify that P the initial population P(0). (a) First substitute P= Pet into the left side of the differential equation. In other words, compute P'. Poet is a sution to the differential equation. Here, Po denotes Use an underscore to write the subscript on Po- (b) Next substitute P= Poe into the right side of the differential equation. In other words, compute aP (c) Are your answers in parts (a) and (b) equal? O Yes O No According to Malthusian population growth (or decay) model, the population of a body changes at a rate proportional to the population at any time. Thus, if P= P(t) is the population at time t, then P' = aP where a is a positive constant. In this exercise, you will verify that P the initial population P(0). (a) First substitute P= Pet into the left side of the differential equation. In other words, compute P'. Poet is a sution to the differential equation. Here, Po denotes Use an underscore to write the subscript on Po- (b) Next substitute P= Poe into the right side of the differential equation. In other words, compute aP (c) Are your answers in parts (a) and (b) equal? O Yes O No

Answer rating: 100% (QA)

Answer I Yes bot... View the full answer