# John D. Blischak(1)

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## Section title

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Text for this sub-sub-heading …Text for this sub-sub-sub-heading …In this section we examine the growth rate of the mean of $$Z_{0}$$, $$Z_{1}$$ and $$Z_{2}$$. In addition, we examine a common modeling assumption and note the importance of considering the tails of the extinction time $$T_{x}$$ in studies of escape dynamics. We will first consider the expected resistant population at $$vT_{x}$$ for some $$v>0$$, (and temporarily assume $$\alpha=0$$)
If we assume that sensitive cells follow a deterministic decay $$Z_{0}(t)=xe^{\lambda_{0}t}$$ and approximate their extinction time as $$T_{x}\approx-\frac{1}{\lambda_{0}}\log x$$, then we can heuristically estimate the expected value as