9514 1404 393
Answer:
221 hours
Explanation:
The population is given by the exponential equation ...
population = (initial value) × (1 +growth rate)^t
where the units of t are the same as the units of growth rate.
This lets us write ...
p(t) = 5000×1.01^t
We want this to be 45000, so ...
45000 = 5000×1.01^t
9 = 1.01^t . . . . . . . . . . . . divide by 5000
log(9) = t×log(1.01) . . . . take logs
t = log(9)/log(1.01) ≈ 220.8
It will take about 221 hours for the population to reach 45000.