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