Answer:
16.8 hours
Explanation:
An exponential population increase can be modeled by the function ...
p(t) = a·b^(t/p)
where 'a' is the initial value (at t=0), b is the multiplier in time period p.
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setup
The colony increased by a factor of b = 80/50 = 1.6 in p = 3 hours. Since we want to find the additional time to reach a population of 1119, the initial population we're working with is 80, not 50.
p(t) = 80·1.6^(t/3)
1119 = 80·1.6^(t/3)
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solution
Solving this for t, we find ...
1119/80 = 1.6^(t/3) . . . . . . . . . . . . divide by 80
log(1119/80) = (t/3)log(1.6) . . . . . take logarithms
t = 3·log(1119/80)/log(1.6) . . . . . divide by the coefficient of t
t ≈ 16.8 . . . . hours
It will take about 16.8 more hours for the population to increase from 80 to 1119.