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

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.

Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.

2 hours earlier than WHAT ?

Your post contains a formulation, which the people will ALWAYS stumble over.

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