<PRE><B>Question 1129948</B>
&lt;br&gt;
{{{f(t) = (45000)/(1+224e^(-0.899t))}}}&lt;br&gt;
NOTE: The exponential e^(-899t) indicates an outbreak that affects all 45000 people in the community in a matter of hours or perhaps minutes, instead of weeks.  I will assume for my answer that the exponential is supposed to be e^(-0.899t).&lt;br&gt;
(a) At the outbreak of the epidemic, t (the number of weeks after the outbreak) is 0, so evaluate f(0):&lt;br&gt;
{{{f(0) = (45000)/(1+224e^(-0.899(0))) = 45000/(1+224(1)) = 45000/225 = 200}}}&lt;br&gt;
ANSWER: 200 people had the flu at the outbreak.&lt;br&gt;
(b) Half the population is 22500, so we want to find t when f(t)=22500.&lt;br&gt;
{{{22500 = (45000)/(1+224e^(-0.899t))}}}&lt;br&gt;
{{{1+224e^(-0.899t) = 45000/22500 = 2}}}&lt;br&gt;
{{{224e^(-0.899t) = 1}}}&lt;br&gt;
{{{e^(-0.899t) = 1/224}}}&lt;br&gt;
{{{-0.899t = ln(1/224)}}}&lt;br&gt;
{{{t = (ln(1/224))/-0.899}}}&lt;br&gt;
which to 5 decimal places is 6.01963&lt;br&gt;
ANSWER: Half the town will be infected after a little more than 6 weeks.</PRE>