Answer:
a). 8100 bacteria
b). 519 bacteria
c). Infinite
Step-by-step explanation:
Population growth of a bacteria is given by the exponential function,
f(x) = [tex]P_{0}(1+\frac{r}{100})^{t}[/tex]
Where f(x) = Population after time 't'
[tex]P_{0}[/tex] = Initial population
r = Growth rate
t = Duration after t hours
If "100 bacteria gets tripled every hour"
300 = [tex]100(1+\frac{r}{100})^{1}[/tex]
3 = 1 + [tex]\frac{r}{100}[/tex]
r = 100×(3 - 1)
r = 200
So the function is, f(x) = [tex]100(3)^{t}[/tex]
a). Population after 4 hours,
f(4) = [tex]100(3)^{4}[/tex]
= 8100 bacteria
b). Population after 90 minutes Or 1.5 hours
f(1.5) = [tex]100(3)^{1.5}[/tex]
= 519.61
≈ 519 bacteria
c). Population after 72 hours,
f(72) = [tex]100(3)^{72}[/tex]
= Infinite