# math

posted by Patty

A colony of bacteria is growing exponentially, increasing in size from 200 to 500 cells in 100 minutes will it take the colony to double in size?

1. Steve

p = ae^kt
500 = 200e^100k
2.5 = e^100k
ln 2.5 = 100k
k = ln2.5/100

p = 200e^(ln2.5/100 t)
= 200*2.5^t/100

to double,
2 = 2.5^t/100
ln 2 = (t/100)ln2.5
t = 100 * ln2/ln2.5 = 75.65 minutes

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