kevinsheng
New Member
- Joined
- Aug 18, 2007
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- 2010
Heya every1.
These problems are from the Jones and Couchman 3 unit maths book 2, and is part of further exponential problems. Im having trouble showing the below and help would be gladly appreciated
1.[FONT="] [/FONT]<!--[endif]-->In actual population studies the rate of growth is given by dP/dt=kP(1-RP) where k, R are constants. This reflects limitations on growth, such as by lack of food and the existence of predators. This is called the logistical growth equation.
Show by differentiation that P= (I) / ((RI+(1-RI)e^(-kt)) where I is the initial population (a constant), is a solution of the logistic equation. <o
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<!--[if !supportLists]-->2.[FONT="] [/FONT]<!--[endif]-->An isolated insect population is attached to a single plant which has a carrying capacity of 100 insects. Its logistic law of growth is given by dP/dt=0.001P(100-P).
Show by substitution that P = 100 / 1 + (1/k)e^(-0.1t)
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<o>Thanks
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These problems are from the Jones and Couchman 3 unit maths book 2, and is part of further exponential problems. Im having trouble showing the below and help would be gladly appreciated
1.[FONT="] [/FONT]<!--[endif]-->In actual population studies the rate of growth is given by dP/dt=kP(1-RP) where k, R are constants. This reflects limitations on growth, such as by lack of food and the existence of predators. This is called the logistical growth equation.
Show by differentiation that P= (I) / ((RI+(1-RI)e^(-kt)) where I is the initial population (a constant), is a solution of the logistic equation. <o
></o><!--[if !supportLists]-->2.[FONT="] [/FONT]<!--[endif]-->An isolated insect population is attached to a single plant which has a carrying capacity of 100 insects. Its logistic law of growth is given by dP/dt=0.001P(100-P).
Show by substitution that P = 100 / 1 + (1/k)e^(-0.1t)
<o
> </o><o
>Thanks </o
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