Question: Begin with bt wild type and m, mutants. Find the discrete-time dynamical system for the fraction pt of mutants. Find the equilibrium fraction of mutants.

Begin with bt wild type and m, mutants. Find the discrete-time dynamical system for the fraction pt of mutants. Find the equilibrium fraction of mutants. Cobweb starting from the initial condition in Exercise 25. Is the equilibrium stable?
This section has ignored the important evolutionary force of mutation. This series of problems builds models that consider mutation without reproduction. Suppose that 20% of wild-type bacteria transform into mutants and that 10% of mutants transform back into wild type ("revert"). In each case, find the following.
a. The number of wild type bacteria that mutate and the number of mutants that revert.
b. The number of wild-type bacteria and the number of mutants after mutation and reversion.
c. The total number of bacteria before and after mutation. Why is it the same?
d. The fraction of mutants before and after mutation.

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