A model predicts that the population of Bergen was 15,000 in 2005 . The model also predicts that each year

Question

A model predicts that the population of Bergen was 15,000 in 2005 . The model also predicts that each year for the next 5 years, the population p increased by 4 % of the previous year's population. Which equation best represents this model, where x is the number of years after 2005 , for x &#8804; 5 ?

Accepted Answer

Choice D is correct. It's given that a model predicts the population of Bergen in 2005 was 15,000 . The model also predicts that each year for the next 5 years, the population increased by 4 % of the previous year's population. The predicted population in one of these years can be found by multiplying the predicted population from the previous year by 1.04 . Since the predicted population in 2005 was 15,000 , the predicted population 1 year later is 15,000 ( 1.04 ) . The predicted population 2 years later is this value times 1.04 , which is 15,000 1.04 1.04 , or 15,000 1.04 2 . The predicted population 3 years later is this value times 1.04 , or 15,000 1.04 3 . More generally, the predicted population, p , x years after 2005 is represented by the equation p = 15,000 1.04 x . Choice A is incorrect. Substituting 0 for x in this equation indies the predicted population in 2005 was 0.96 rather than 15,000 . Choice B is incorrect. Substituting 0 for x in this equation indies the predicted population in 2005 was 1.04 rather than 15,000 . Choice C is incorrect. This equation indies the predicted population is decreasing, rather than increasing, by 4 % each year.

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