# Exponential Growth and Decay General Problems

Suppose you put one bacterium on a petri plate containing a suitable medium at a favourable temperature. Assume that there will be a doubling every 20 minutes. How many would you expect to find after 24 hours?

First let's look at a film of the growth as prepared with time lapse photography.

If the bacteria double three times per hour, then for every one at the beginning of an hour there will be two at 20 minutes, four at 40 minutes, and eight at 1 hour. Calculate the magnitude of the growth constant:

A. \(0.0347\; \mathrm h^{-1}\)

B. \(0.0867\; \mathrm h^{-1}\)

C. \(0.693\; \mathrm h^{-1}\)

D. \(1.10\; \mathrm h^{-1}\)

E. \(2.08\; \mathrm h^{-1}\)

A. \(0.0347\; \mathrm h^{-1}\) - No. You have mistaken hours for minutes.

B. \(0.0867\; \mathrm h^{-1}\) - No. The doubling time is 20 min or 1/2 hr.

C. \(0.693\; \mathrm h^{-1}\) - No. The doubling time is not 1 hr.

D. \(1.10\; \mathrm h^{-1}\) - No. The doubling time is 20 min or 1/2 hr.

**E. \(2.08\; \mathrm h^{-1}\) - Correct!**