Two months from now, the population of a colony of insects

BTGmoderatorDC wrote:Two months from now, the population of a colony of insects in a remote area will reach 3.2 * 10^4. If the population of the colony doubles every two months, what was the population eight months ago?

a) 3.6 * 10^2
b) 1.0 * 10^3
c) 2.0 * 10^3
d) 1.6 * 10^4
e) 2.6 * 10^4

OA B

Source: Veritas Prep

Given: Population in 2 months from now = 3.2 * 10^4;

Question: What's the population 8 months ago?

So, we have to find out the population 10 months ago from the point when the population would be 3.2 * 10^4.

Since the population doubles every 2 months, it will have 10/2 = 5 periods of compounding. Thus, the population would have been 1/2^5 = 1/32 times 8 months ago.

Thus, population 8 months ago = (3.2 * 10^4) / 32 = (32 * 10^3) / 32 = 10^3

The correct answer: B

Hope this helps!

-Jay
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BTGmoderatorDC wrote:Two months from now, the population of a colony of insects in a remote area will reach 3.2 * 10^4. If the population of the colony doubles every two months, what was the population eight months ago?

a) 3.6 * 10^2
b) 1.0 * 10^3
c) 2.0 * 10^3
d) 1.6 * 10^4
e) 2.6 * 10^4

OA B

Source: Veritas Prep

Let's use a growth table to work backwards

If the population DOUBLES every 2 months we travel into the future, we can also say that the population is HALVED every 2 months we travel into the past

2 months from now: population = (3.2)(10^4)
Now: population = (1/2)(3.2)(10^4) = (1.6)(10^4)
2 months ago: population = (1/2)(1.6)(10^4) = (0.8)(10^4)
4 months ago: population = (1/2)(0.8)(10^4) = (0.4)(10^4)
6 months ago: population = (1/2)(0.4)(10^4) = (0.2)(10^4)
8 months ago: population = (1/2)(0.2)(10^4) = (0.1)(10^4)

(0.1)(10^4) isn't among the answer choices, so let's REWRITE it.

(0.1)(10^4) = (1)(10^-1)(10^4)
= (1)(10^3)

Answer: B

BTGmoderatorDC wrote:Two months from now, the population of a colony of insects in a remote area will reach 3.2 * 10^4. If the population of the colony doubles every two months, what was the population eight months ago?

a) 3.6 * 10^2
b) 1.0 * 10^3
c) 2.0 * 10^3
d) 1.6 * 10^4
e) 2.6 * 10^4

OA B

Source: Veritas Prep

The population currently must be 3.2 * 10^4 / 2 = 1.6 * 10^4. So, 2 months ago, the population was 1.6 * 10^4 / 2 = 0.8 * 10^4; 4 months ago, the population was 0.8 * 10^4 / 2 = 0.4 * 10^4; 6 months ago, the population was 0.4 * 10^4 / 2 = 0.2 * 10^4; and, 8 months ago, the population was 0.2 * 10^4 / 2 = 0.1 * 10^4 = 1.0 * 10^3.

Answer: B