# Math Insight

### Image: Change in bacteria population density as a function of bacteria population density

Changes in experimental measurements of bacteria population density are plotted versus the population density at the beginning of the interval. The data was taken from the following table with time rescaled so that each snapshot was one unit of time.

Measurements of bacterial density at pH 6.25.
The units of “Population Density” are those of absorbance as measured by a spectrophotometer.
Time (min)Time Index
$t$
Population Density
$B_t$
Pop Change/Unit Time
$B_{t+1}\nobreak{-}B_t$
000.0220.014
1610.0360.024
3220.0600.041
4830.1010.068
6440.1690.097
8050.266

Image file: bacteria_density_change_versus_density.png

Source image file: bacteria_density_change_versus_density.ggb
Source image type: Geogebra