SOLUTION: A culture of bacteria triples every 8 hours. if there are 100 bacteria now, and 2700 bacteria after 24 hours, find the bacteria population 2 hours earlier
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-> SOLUTION: A culture of bacteria triples every 8 hours. if there are 100 bacteria now, and 2700 bacteria after 24 hours, find the bacteria population 2 hours earlier
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Question 1188722: A culture of bacteria triples every 8 hours. if there are 100 bacteria now, and 2700 bacteria after 24 hours, find the bacteria population 2 hours earlier Found 2 solutions by Theo, ikleyn:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the bacteria triples every 8 hours.
there are 100 now.
there are 300 in 8 hours.
there are 900 in 16 hours.
there are 2700 in 24 hours.
the growth is exponential.
let x = the rate of growth each hour.
you get 300 = 100 * x^8
divide both sides by 100 to get:
3 = x^8
solve for x to get:
x = 3 ^ (1/8) = 1.14720269.
that's the rate of growth every hour.
in 8 hours, the number of bacteria grows from 100 to 100 * 1.14720269 ^ 8 = 300.
in 16 hours, the number of bacteria grows from 100 to 100 * 1.14720269 ^ 16 = 900.
in 24 hours, the number of bacteria grows from 100 to 100 * 1.14720269 ^ 24 = 2700.
in 22 hours, the number of bacteria grows from 100 to 100 * 1.14720269 ^ 22 = 2051.556351.
that's your solution.
the equation can be graphed as shown below.
coordinate points are in (x,y) format.
x is the number of hours.
y is the number of bacteria.
