OG详解-OG9 数学2 Q11

Choice C is correct. It’s given that the relationship between t and n is exponential. The table shows that the value of n increases as the value of t increases. Therefore, the relationship between t and n can be represented by an increasing exponential equation of the form n = a(1+b)^t , where a and b are positive constants. The table shows that when t = 0, n = 604. Substituting 0 for t and 604 for n in the equation n = a(1+b)^t  yields 604 = a(1+b)⁰ , which is equivalent to 604 = a(1), or 604 = a. Substituting 604 for a in the equation n = a(1+b)^t  yields n = 604(1 +b)^t. The table also shows that when t = 1, n = 606.42. Substituting 1 for t and 606.42 for n in the equation n = 604(1+b)^t yields 606.42 = 604(1+b)¹, or 606.42 = 604(1+b). Dividing both sides of this equation by 604 yields approximately 1.004 = 1+b. Subtracting 1 from both sides of this equation yields that the value of b is approximately 0.004. Substituting 0.004 for b in the equation n = 604(1+b)^t  yields n = 604(1+0.004)^t. Therefore, of the choices, choice C best represents the relationship between t and n.
Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.