Four hours from now, the population of a colony of bacteria will reach \(1.28*10^6.\) If the population of the colony

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Mon Feb 21, 2022 7:10 am

Official Guide

Four hours from now, the population of a colony of bacteria will reach \(1.28*10^6.\) If the population of the colony doubles every \(4\) hours, what was the population \(12\) hours ago?

A. \(6.4*10^2\)
B. \(8.0*10^4\)
C. \(1.6*10^5\)
D. \(3.2*10^5\)
E. \(8.0*10^6\)

OA B

Let's work backwards.

Population 4 hours in future: 1.28 x 10^6
Population now: 0.64 x 10^6 (half the population 4 hours in future)
Population 4 hours ago: 0.32 x 10^6 (half the current population)
Population 8 hours ago: 0.16 x 10^6 (half the population 4 hours ago)
Population 12 hours ago: 0.08 x 10^6 (half the population 8 hours ago)

Now check the answer choices.
Only answer choices B and E have the same format with 8 times some power of 10
Answer choice E definitely doesn't match, so the correct answer must be B

For any doubters out there, notice that:
0.08 x 10^6 = (8.0) x (10^-2) x 10^6
= 8.0 x 10^4

Answer: B