# Math

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Bacteria A has an initial population of 500 and doubles everyday. Bacteria B has an initial population of 50 and triples everyday. How long will it take the population of bacteria B to overtake the population of bacteria A

• Math -

B starts out less than A, but after x days catches up when

50*3^x = 500*2^x
log50 + xlog3 = log500 + xlog2
x(log3-log2) = log10 = 1
x = 1/log(3/2) = 5.68

check:
A: 500 1000 2000 4000 8000 16000 32000 ...
B: 50 150 450 1350 4050 12150 36450 ...

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