SOLUTION: an experimental culture has an initial population of 50 bacteria. the population increased by 80% every 20 minutes. determine the time it will take to have a population of 1.2 mill

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Question 1102431: an experimental culture has an initial population of 50 bacteria. the population increased by 80% every 20 minutes. determine the time it will take to have a population of 1.2 million bacteria.
Answer by greenestamps(13200) About Me  (Show Source):
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If the population increases by 80%, it grows by a factor of 1.80. So the expression 50%281.80%29%5En is the population after "n" 20-minute periods. You want to know when the population will reach 1.2 million.

With the variable in the exponent, you will need to use logarithms to solve the problem.

50%281.80%29%5En+=+1200000
1.80%5En+=+1200000%2F50+=+24000
n%2Alog%281.80%29+=+log%2824000%29
n+=+log%2824000%29%2Flog%281.80%29+=+17.159

17.159%2A20+=+343 to the nearest whole number.

The population of bacteria will reach 1.2 million after about 343 minutes.