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A culture of bacteria doubles every 2 hours. if there are 500 bacteria at the beginning, how many bacteria will there be after 24 hours?



Answer :

vargheseryan1279

This question is exponential; the basic formula is
(final amount) = (initial amount) * 2^(total hours ÷ time it takes to double) 

So if F = final amount and t = time in hours, 
[tex]F=500*2^ \frac{t}{2} [/tex]

and for this one, 
[tex]F=500*2^ \frac{24}{2} [/tex]

[tex]F=500*2^1^2[/tex]

[tex]F = 2048000 [/tex]

naǫ
There are 500 bacteria at the beginning and they double every 2 hours. So, if you want to find the number of the bacteria after 2 hours, you must multiply 500 by 2; after 4 hours - multiply 500 by 4; after 6 hours - multiply 500 by 8; etc.
You can write it like this:
[tex]x=500 \times 2^{\frac{t}{2}}[/tex]
where x is the number of the bacteria after t hours

[tex]t=24 \\ \\ x=500 \times 2^\frac{24}{2}=500 \times 2^{12}=500 \times 4096=2048000[/tex]

There will be 2,048,000 bacteria after 24 hours.

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