Suppose that the number of cells in a tumor doubles every 5 months. considering that the tumor begins with a single cell, answer the following: how many cells will there be after 3 years? 5 years?

Let's call a 5-month period a "pent", so the conversion from years to pents is 1 year for every 2.2 pents.

Then



and



Now, if the number of cells doubles every pent, and if denotes the number of cells after pents, then the number of cells is modeled recursively by



starting with .

Solving explicitly for , you arrive at



or,



So, after 6.6 pents (3 years), you should expect the number of cells to grow to about . After 11 pents (5 years), you should find cells.

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