AAPL wrote: ↑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