[tex]

\frac{{dx}}{{dt}} = k\left( {150000 - x\left( t \right)} \right)

[/tex]

At t=0, 30000 people are infected, and at t=15, 60000. How long will it take for 120000 are infected? Here is my work:

[tex]

\begin{array}{l}

x\left( t \right) = 30000 \cdot e^{k \cdot t} \\

x\left( {15} \right) = 30000 \cdot e^{k \cdot 15} = 60000 \\

\Rightarrow k = 0,046 \\

x\left( t \right) = 30000 \cdot e^{0,046 \cdot t} = 120000 \\

\end{array}

[/tex]

Problem is that this leads to no good, the answer is supposed to be about t=72 (days), but I'm not sure how to implement the 150000 in the beginning (at least I think that's the prob)...anyone?