A colony of 100,000 ants has been declining in number at a rate of 11.4% per month. If allowed to decline uninhibited, how long will it take the population to decrease to 25,000 ants? Round to the nearest tenth.

a. 17.6 months
b. 12.2 months
c. 5.3 months
d. 24.3 months

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Answer:

b. 12.2 months

A percentage is a way to describe a part of a whole. The correct option is B.

What are Percentages?

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given that the colony of 100,000 ants has been declining in number at a rate of 11.4% per month. Therefore, the number of months it will take for the ant population to reach 25,000 ants is,

Population = 100,000(1-0.114)ⁿ

25,000 = 100,000(1-0.114)ⁿ

0.25 = 0.886ⁿ

log(0.25) / log(0.886) = n

n = 11.45335

Since the value is close to 12.2 months.

Hence, the correct option is B.

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