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Math Help - Mathematical Modelling through ODE

  1. #1
    Member kjchauhan's Avatar
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    Mathematical Modelling through ODE

    Please help to solve the following :

    "Cigarette consumption in a country increased from 50 per capita in 1900 AD to 3600 per capita in 1960 AD. Assuming that the growth in consumption follows a logistic law with a limiting consumption of 4000 per capita, estimate the consumption per capita in 1950."

    Thanks in advance.
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  2. #2
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    If \displaystyle P = P(t) is the population who smoke at any year with a carrying capacity (limiting population) of \displaystyle K, then the logistic model is

    \displaystyle \frac{dP}{dt} = rP\left(1 - \frac{P}{K}\right)

    a separable DE.

    Solve the DE, then use the two points you have been given to solve for \displaystyle r and your integration constant.
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