P t = 290 1.04 4 6 t The function P models the population, in thousands, of a certain city

Question

P t = 290 1.04 4 6 t The function P models the population, in thousands, of a certain city t years after 2005 . According to the model, the population is predicted to increase by n % every 18 months. What is the value of n ?

Accepted Answer

Choice C is correct. It's given that the function P models the population of the city t years after 2005 . Since there are 12 months in a year, 18 months is equivalent to 18 12 years. Therefore, the expression 18 12 x can represent the number of years in x 18 -month periods. Substituting 18 12 x for t in the given equation yields P 18 12 x = 290 1.04 4 6 18 12 x , which is equivalent to P 18 12 x = 290 1.04 x . Therefore, for each 18 -month period, the predicted population of the city is 1.04 times, or 104 % of, the previous population. This means that the population is predicted to increase by 4 % every 18 months. Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect. Each year, the predicted population of the city is 1.04 times the previous year's predicted population, which is not the same as an increase of 1.04 % . Choice D is incorrect and may result from conceptual or calculation errors.

Question p-t-29