# Math Help - Exponential Bacteria

1. ## Exponential Bacteria

Suppose that a bacterial culture is growing exponentially and the culture doubles every 12 hours. Obtain a formula for the number Pn of square millimeters of culture expected in n hours given that the culture measured 5 square millimeters when first observed.

2. Originally Posted by WartonMorton
Suppose that a bacterial culture is growing exponentially and the culture doubles every 12 hours. Obtain a formula for the number Pn of square millimeters of culture expected in n hours given that the culture measured 5 square millimeters when first observed.
If we assume that when the population doubles the area it occupies is also doubled we can reason as follows: after n hours, there have been n/12 doublings, therefore we get an area of $P_n = 2^{n/12}\cdot 5\mathrm{mm}^2=\left(2^{1/12}\right)^n\cdot 5\mathrm{mm}^2\approx 1.0595^n\cdot 5\mathrm{mm}^2$.