My question is a bacteria increases its number every hour by eight times (eight times more bacteria than the last hour) in 12 hours how much bacteria will there be? I also have to use this formula (y=1x8^t) where t is the hours.
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Answer:
The rate of exponential growth of a bacterial culture is expressed as generation time, also the doubling time of the bacterial population. Generation time (G) is defined as the time (t) per generation (n = number of generations). Hence, G=t/n is the equation from which calculations of generation time (below) derive.
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Step-by-step explanation:
It is given that the number of bacteria doubles every hour.
Therefore, the number of bacteria after every hour will form a G.P.
with first term (a=30) and common ratio (r=2)
∴a
3
=ar
2
=(30)(2)
2
=120
Therefore, the number of bacteria at the end of 2nd hour will be 480.
a
5
=ar
4
=(30)(2)
4
=480
and a
n+1
=ar
n
=(30)(2)
n
Thus the number of bacteria at the end of nth hour will be (30)(2)
n
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