Answer:
t ≈ 44.43 hours
Step-by-step explanation:
Expression that models the population of a bacteria after time 't' is,
N(t) = [tex]250(e^{0.0156t})[/tex]
Here initial population = 250
And N(t) = Population after 't' hours
t = duration
We have to find the duration in which bacterial population gets doubled.
N(t) = 2×250 = 500
From the given expression,
500 = [tex]250(e^{0.0156t})[/tex]
[tex]e^{0.0156t}=2[/tex]
[tex]\text{ln}(e^{0.0156t})=\text{ln}(2)[/tex]
0.0156t[ln(e)] = 0.693147
0.0156t = 0.693147
t = [tex]\frac{0.693147}{0.0156}[/tex]
t = 44.432
t ≈ 44.43 hours
