# Math Help - Mathematical Modelling through ODE

1. ## 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.

2. 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.