Formula for growth or decay
R= \(R_{0}[1 \pm \frac{r}{100}]^t\)
R= Final population of Bacteria
\(R_{0}\)= Initial Population
r = Rate of growth or decay
t= Time period
\(R_{0}\)= 103 bacteria
when, t=2
R becomes 103 × 2= 206 bacteria
Substituting these values in the formula of growth
206 = 103 × \((1+ \frac{r}{100})^2\)
Dividing both sides by 103, we get
2 = \((1+ \frac{r}{100})^2\)
\((1+ \frac{r}{100})\)= √2------(1)
\((1+ \frac{r}{100})\)= 1.414
r = (1.414 -1) × 100= .414 × 100= 41.4%
Number of bacteria at the end of 6 hours = 103 × \((1+ \frac{r}{100})^6\)= 103 × \([\sqrt{2}]^6\) ------Using (1)
= 103 × 2³
=103 × 8
= 824→→bacteria that Harriet have in the dish at the end of 6 hours
