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Suppose we model the spread of a virus in a certain population as follows. On day one, $\\var{a}$ people are infected. On each subsequent day, each infected person gives the cold to $\\var{b}$ others.

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How many people are infected by day 2? [[0]]

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How many people are infected by day 3? [[1]]

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How many people are infected by day 4? [[2]]

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Given the following recurrence relation for the number of people infected by day n, find A and B:

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\$C(n)=\\begin{cases} A & if & n=1\\\\ C(n-1) + [C(n-1) \\times B] & if & n\\geq2 \\end{cases}\$

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A = [[0]] and B = [[1]]

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