OG详解-OG5 数学2 Q25

Choice A is correct. It’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 ​23​of a year. It’s given that the population is predicted to increase by 4% every n months. Since there are 12 months in a year,  ​23​ 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)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)t, not P(t) = 260(1.04)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)t, not P(t) = 260 (1.04)t.