SOLUTION: A population of bacteria triples every five days. If the initial population is one thousand, then by what factor will the population have increased in the first ten days? At what t

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Question 640953: A population of bacteria triples every five days. If the initial population is one thousand, then by what factor will the population have increased in the first ten days? At what time t, in days will the population have increased by a factor of 6?
my problem is i don't know what formula to use and i don't know what a factor is :/

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the initial population = +p+
After 5 days +3p+
After 10 days +9p+
After 15 days +27p+
After 20 days +81p+
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If n = 1,2,3,4,5, ( any whole positive number )
After +5n+ days, population = +p%2A3%5En+
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By factor, they mean what is the multiplier?
If +p+=+1000+ and
+5n+=+10+
+n+=+2+
+p%2A3%5En+=+1000%2A3%5E2+
+p%2A3%5En+=+9000+
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What factor do you multiply 1000 by to get 9000 ?
The factor is +9+
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At what time t, in days will the population have increased by a factor of 6?
+6%2A1000+=+6000+
They want days, which is +t+=+5n+
+1000%2A3%5En+=+6000+
+3%5En+=+6+
Take the log base 10 of both sides
+log%28+3%5En+%29+=+log%28+6+%29+
+n%2Alog%283%29+=+log%286%29+
+n+=+log%286%29+%2F+log%283%29+
+t+=+5n+
+t+=+5%2A%28+log%286%29+%2F+log%283%29%29+
Calculate the logs, do the division, and
round off to the nearest day