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**Robb** The number $\displaystyle y$ of persons infected by a highly contagious diesease is modelled by a so-called logistic curve;

$\displaystyle y = \frac {L}{1+ Me^{-kt}}$,

where t is the time measured in months from when the outbreak of the disease was discovered. At that time there were 200 infected persons, and after one month there were 1,000 infected. Eventually the number levelled out at 10,000.

(a) Show that $\displaystyle y$ satisfies the logistic equation

$\displaystyle \frac {dy}{dt} = ky(1-\frac {y}{L})$.

(b) Find the values of hte parameters L,M, and k of the model.