Suppose that the bacteria in a colony grow unchecked according to the Law of Exponential Change. The colony starts with 1 bacterium and triples in number every 20 minutes. How many bacteria will the colony contain at the end of 24 ​hours?

Answer: There are 2.25×10³⁴ bacteria at the end of 24 hours.Step-by-step explanation:Since we have given that Number of bacteria initially = 1It triples in number every 20 minutes.So, [tex]\dfrac{20}{60}=\dfrac{1}{3}[/tex]So, our equation becomes[tex]y=y_0e^{\frac{1}{3}k}\\\\3=1e^{\frac{1}{3}k}\\\\\ln 3=\dfrac{1}{3}k\\\\k=\dfrac{1.099}{0.333}=3.3[/tex]We need to find the number of bacteria that it will contain at the end of 24 hours.So, it becomes,[tex]y=1e^{24\times 3.3}\\\\y=e^{79.1}\\\\y=2.25\times 10^{34}[/tex]Hence, there are 2.25×10³⁴ bacteria at the end of 24 hours.