Insect Population Growth

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Each year for 4 years, an insect species increased its population within a locality by the number equal to half of the population of the preceding year. If there were 16,200 insects of the species in the locality at the end of the four-year period, how many insects of the species were in the locality at the beginning of the four-year period?

Review: Insect Population Growth


Explanation

The question is telling us that, if the population in a given year was 100, then in the next year it increased by to 150. Or, if it was x in a given year, it increased by to in the following year. One way of working this problem would be to make a table of the insect count per year, and work it either backward from 16,200, or forward from a variable. Another way to approach this question is to think of it as a compound interest formula. (It's compound because the new insects beget more insects each year.) The formula is a bit faster. We are measuring between the beginning and the end of a 4-year period, so we have 4 full years of growth. Therefore, if we think of our initial population - or "principal," in investment terms - as P, the total growth is captured by:









The digits 1 + 6 + 2 + 0 + 0 = 9, so 16,200 is divisible by 9.







The correct answer is (D).


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