# Math Insight

### Image: Bacteria population density as a function of time, for a long time period

Experimental data from measurements of bacteria population density are plotted versus time index (blue points). Predictions of an exponential growth model that was fit to the first five points are shown by the red X's. 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
000.022
1610.036
3220.060
4830.101
6440.169
8050.266
9660.360
11270.510
12880.704
14490.827
160100.928

Image file: bacteria_density_versus_time_long.png

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