# Answer to Question #3674 in Algebra for tami

Question #3674

A culture of bacteria grew from 320 to 780 in 5 hours. If this growth continues at this rate then how long will it take the population to triple

Expert's answer

Bacteria culture grows according the law:

A = A0 e^kt

Let's construct the system of equations

780 = 320 e

780*3 = 780 e

5k = ln(780/320)

k = 0.178

3 = e

t = ln 3 / 0.178 = 6.165 hours

A = A0 e^kt

Let's construct the system of equations

780 = 320 e

^{5k}780*3 = 780 e

^{kt}5k = ln(780/320)

k = 0.178

3 = e

^{ 0.178 t}t = ln 3 / 0.178 = 6.165 hours

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## Comments

dena20.07.11, 18:38This is actually 6.712 and if you calculate out 80/13 - you get 6.15....just depends on how picky your professor is.

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