Question

Bacteria can multiply at an alarming rate when each bacteria splits into two new cells, thus doubling. If we start with only one bacteria which can double every hour, how many bacteria will we have by the end of the day? Show your work

Answer 1

Answer:

2^24 = 16,777,216 bacterias.

Step-by-step explanation:

So we start with 1 bacteria

after 1 hours: 2*1 = 2

after 2 hours: 2*2 = 2^2 = 4

after 3 hours: 2*2^2 = 2^3  

after n hours: 2^n  

Since one day has 24 hours we have n = 24 and total number of bacteria will

be:  2^24 = 16,777,216 bacterias.

Answer 2

There will be 16,777,216 bacteria by the end of the day.

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This situation can be represented by a geometric sequence, in which the quotient of consecutive terms is always the same, called common ratio.

The nth term of a geometric sequence is:

$a_n = a_0q^n$

In which $a_0$ is the term at the initial moment and q is the common ratio.

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• Initially, 1 bacteria, which means that $a_0 = 1$
• Double every hour, thus, $q = 2$

After n hours, the amount of bacteria will be given by:

$a_n = 2^{n}$

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By the end of the day, that is, 24 hours, the amount will be:

$a_{24} = 2^{24} = 16777216$

There will be 16,777,216 bacteria by the end of the day.

A similar question is given at https://brainly.com/question/23826475