Cells, growing old
In conditions of abundant food supply, bacteria like Escherichia coli and Pseudomonas aeruginosa reproduce by dividing into two identical daughter cells at regular intervals \(T_d\), referred to as their doubling time. Assume that a large number of E. coli are growing in a batch culture with abundant food supply and that they've reached a steady state, i.e. the fraction of cells that are \(x\%\) of a doubling time old, \(\displaystyle\phi_x\), is constant in time. To the nearest minute, what is the age of the average cell if the doubling time is 60 minutes?