SOLUTION: A particular type of bacteria known to be present in cake mix grows continuously at a rate of 10% per day. There are approximately 500 bacteria in the mix when its packaged. how lo

Question 515931: A particular type of bacteria known to be present in cake mix grows continuously at a rate of 10% per day. There are approximately 500 bacteria in the mix when its packaged. how long does it take for the bacteria to reach 4,000,000
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A particular type of bacteria known to be present in cake mix grows continuously at a rate of 10% per day.
There are approximately 500 bacteria in the mix when its packaged.
how long does it take for the bacteria to reach 4,000,000
:
A multiplier for a 10% increase = 1.1
:
let t = no. of days for this to happen
;
500*(1.1^t) = 4000000
divide both sides by 500, results
1.1^t = 8000
use logs here
log(1.1^t) = log(8000)
the log equiv of exponents
t*log(1.1) = log(8000)
divide both sides by log(1.1)
t = ; use a calc on this
t = 94.3 days
:
:
Check this: enter into a calc: 500*1.1^94.3 ~ 4000000
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