if a certain bacteria population triples in 3 hours, determine the time t in hours for the population to double.

Answer 1

Let y = population of bacteria

Let a = initial population of bacteria

y = a(3)^t/3 The trick here is divide the t by 3. When "t" is 3 hours, "a" gets multiplied by 3.

The population has doubled when y = 2a.

2a = a(3)^t/3

2 = (3)^t/3

log₃(2) = log₃((3)^t/3)

log₃(2) = (t/3)*log₃(3)

log₃(2) = t/3

3*log₃(2) = t

3*(log 2)/(log 3) = t (with change-of-base formula to base 10 logarithms)

1.893 = t

The population will double in about 1.9 hours.