P t = 260 1.04 6 4 t The function P models the population, in thousands, of a certain city

Question

P t = 260 1.04 6 4 t The function P models the population, in thousands, of a certain city t years after 2003 . According to the model, the population is predicted to increase by 4 % every n months. What is the value of n ?

Accepted Answer

Choice A is correct. It&rsquo;s given that the function P models the population, in thousands, of a certain city t years after 2003 . The value of the base of the given exponential function, 1.04 , corresponds to an increase of 4 % for every increase of 1 in the exponent, 6 4 t . If the exponent is equal to 0 , then 6 4 t = 0 . Multiplying both sides of this equation by 4 6 yields t = 0 . If the exponent is equal to 1 , then 6 4 t = 1 . Multiplying both sides of this equation by 4 6 yields t = 4 6 , or t = 2 3 . Therefore, the population is predicted to increase by 4 % every 2 3 of a year. It&rsquo;s given that the population is predicted to increase by 4 % every n months. Since there are 12 months in a year, 2 3 of a year is equivalent to 2 3 12 , or 8 , months. Therefore, the value of n is 8 . Choice B is incorrect. This is the number of months in which the population is predicted to increase by 4 % according to the model P t = 260 1.04 t , not P t = 260 1.04 6 4 t . Choice C is incorrect. This is the number of months in which the population is predicted to increase by 4 % according to the model P t = 260 1.04 4 6 t , not P t = 260 1.04 6 4 t . Choice D is incorrect. This is the number of months in which the population is predicted to increase by 4 % according to the model P t = 260 1.04 1 6 t , not P t = 260 1.04 6 4 t .

Question p-t-26