SOLUTION TO PROBLEM 5

Let us see how the number of viruses and bacteria changes in time. Denote by $t = 0, 1, 2, 3,\ldots$ the minutes, by V(t) the number of viruses at time t, and by B(t) the number of bacteria at time t.

We get that

$$\begin{array}{lcl} V(0) = 1, &\qquad& B(0) = n\\ V(1) = 2, &... ...1) = 2(n-1)\\ V(2) = 2^2, &\qquad& B(2) = 2^2(n-2) \end{array}$$

and so on $\ldots$. In general,

$$V(t) = 2^t, \qquad B(t) = 2^t(n-t).$$

Observe that for t = n, the number of bacteria is

B(n) = 2ⁿ(n-n) = 0,

so the colony dies out in n minutes.

Questions and/or comments should be directed to Judy Downey or Griff Elder

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Last modified:   Thu Sep 27 19:25:29 CDT 2001