SOLUTION: really need help and the step by step question reads... In a colony of bacteria growing in a nutrient solution, the number of bacteria grows exponentially, and it doubles every 3

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Question 752776: really need help and the step by step
question reads...
In a colony of bacteria growing in a nutrient solution, the number of bacteria grows exponentially, and it doubles every 30 minutes. If the number of bacteria is initially 100,000. how many minutes will it take for the number of bacteria to reach 1,000,000 Round answer to nearest tenth of a minute.
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Continuous exponential growth A=p%2Ae%5E%28kt%29 where A is amount at time t and p is the initial amount for t=0.

Doubles every 30 minutes ---- let us use time units in minutes.
2p=p%2Ae%5E%28k%2A30%29 and we want to have a value found for k.

Divide both sides by p.
2=e%5E%28k%2A30%29
ln%282%29=30k%2Aln%28e%29
ln%282%29=30k
k=%281%2F30%29%2Aln%282%29
highlight%28k=0.023%29

The growth model for this example is highlight%28A=p%2Ae%5E%280.023t%29%29.
t is time in minutes
p is initial population for t=0
A is population at some time t