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juin [17]
2 years ago
10

Suppose that the bacteria in a colony grow unchecked according to the Law of Exponential Change. The colony starts with 1 bacter

ium and triples in number every 20 minutes. How many bacteria will the colony contain at the end of 24 ​hours?
Mathematics
1 answer:
inn [45]2 years ago
3 0

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 = 1

It triples in number every 20 minutes.

So, \dfrac{20}{60}=\dfrac{1}{3}

So, our equation becomes

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

We need to find the number of bacteria that it will contain at the end of 24 hours.

So, it becomes,

y=1e^{24\times 3.3}\\\\y=e^{79.1}\\\\y=2.25\times 10^{34}

Hence, there are 2.25×10³⁴ bacteria at the end of 24 hours.

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