A function p estimates that there were 2,000 animals in a population in 1998 . Each year from 1998 to

Question

A function p estimates that there were 2,000 animals in a population in 1998 . Each year from 1998 to 2010 , the function estimates that the number of animals in this population increased by 3 % of the number of animals in the population the previous year. Which equation defines this function, where p x is the estimated number of animals in the population x years after 1998 ?

Accepted Answer

Choice C is correct. It's given that a function p estimates that there were 2,000 animals in a population in 1998 and that each year from 1998 to 2010 , the number of animals in this population increased by 3 % of the number of animals in the population the previous year. It follows that this situation can be represented by the function p x = a 1 + r 100 x , where p x is the estimated number of animals in the population x years after 1998 , a is the estimated number of animals in the population in 1998 , and each year the estimated number of animals increased by r % . Substituting 2,000 for a and 3 for r in this function yields p x = 2,000 1 + 3 100 x , or p x = 2,000 1.03 x . Choice A is incorrect. This function represents a population in which each year the number of animals increased by 200 % , not 3 % , of the number of animals in the population the previous year. Choice B is incorrect. This function represents a population in which each year the number of animals increased by 97 % , not 3 % , of the number of animals in the population the previous year. Choice D is incorrect. This function represents a population in which each year the number of animals decreased, rather than increased, by 3 % of the number of animals in the population the previous year.

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