Step 1: Set up the microbial death kinetics.
Microbial death under a lethal process (such as heat) typically follows first-order kinetics, so the rate of decline in the surviving population N follows:
\[ \frac{dN}{dt} = -kN \]
Step 2: Convert to logarithmic form.
Integrating and converting to base-10 log gives:
\[ \log N = \log N_0 - \frac{k}{2.303}\, t \]
This is a straight line if \( \log N \) is plotted against t, with slope \( -\frac{k}{2.303} \).
Step 3: Relate the slope to the decimal reduction time.
The decimal reduction time, D, is defined as the time taken for the population to fall by one log cycle (a 90 percent reduction). Setting \( \log N_0 - \log N = 1 \) and solving for t from the line equation shows:
\[ D = -\frac{1}{\text{slope}} = \frac{2.303}{k} \]
Step 4: Final Answer.
The inverse of the slope of the log(survivors) versus time plot is the D value.
\[ \boxed{D = -\dfrac{1}{\text{slope}}} \]