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 4% by of the previous year’s population. Which equation best represents this model, where x is the x ≤ 5 number of years after 2005, for?
Correct answer: D (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice D is correct. It’s given that a model predicts the population of Bergen in 2005 15,000 was . The model also predicts that each year for the next 5 years, 4% the population increased by of the previous year’s population. The predicted population in one of these years can be found by multiplying the predicted 1.04 population from the previous year by . Since the predicted population in 2005 15,000 15,000 1.04 was , the predicted population 1 year later is ^ h. The 1.04 predicted population 2 years later is this value times , which is 15,000 1.04 1.04 15,000 1.04 2 ^ h^ h, or ^ h . The predicted population 3 years later is 1.04 15,000 1.04 3 this value times , or ^ h . More generally, the predicted population, 2005 =15,000 1.04 x p, x years after is represented by the equation p ^ h . Choice A is incorrect. Substituting 0 for x in this equation indicates the predicted 2005 0.96 15,000 population in was rather than . Choice B is incorrect. 2005 Substituting 0 for x in this equation indicates the predicted population in 1.04 15,000 was rather than . Choice C is incorrect. This equation indicates the 4% predicted population is decreasing, rather than increasing, by each year.
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