Set 4: Polynomial Functions (Advanced)

Choice B 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 h. The predicted population 2 years later is this value times 1.04, which is 15,000 ^1.04 h^1.04 h, or 15,000 ^1.04 h 2 . The predicted population 3 years later is this value times 1.04, or 15,000 ^1.04 h 3 . More generally, the predicted population, p, x years after 2005 is represented by the equation p = 15,000 ^1.04 hx . Choice D is incorrect. Substituting 0 for x in this equation indicates the predicted population in 2005 was 0.96 rather than 15,000. Choice C is incorrect. Substituting 0 for x in this equation indicates the predicted population in 2005 was 1.04 rather than 15,000. Choice A is incorrect. This equation indicates the predicted population is decreasing, rather than increasing, by 4% each year.