joyseychow wrote:
The population of locusts in a certain swarm doubles every two hours. If 4 hours ago there were 1,000 locusts in the swarm, in approximately how many hours will the swarm population exceed 250,000 locusts?
A. 6
B. 8
C. 10
D. 12
E. 14
Since the population doubles every 2 hours, we get:
4 hours ago --> 1000
2 hours ago --> 2000
Now --> 4000
Formula for exponential change:
Final amount = (original amount) * (multiplier)^(number of changes)
Since the final amount must exceed 250,000, we get:
(original amount) * (multiplier)^(number of changes) > 250,000Here:
original amount = current amount = 4000
multiplier = 2 (since the population keeps doubling)
x = number of changes
Plugging these values into the blue inequality above, we get::
\(4000 * 2^x > 250,000\)
\(2^x > 62.5\)
Since \(2^6 = 64\), the population must double 6 times.
Since the population doubles every 2 hours, the number of hours required = 2*6 = 12
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