Explanation
Correct answer: A.
Choice A is correct. It is given that the relationship between population and year is linear; therefore, the function that models the population years after is of the form , where is the slope and is the population when . In the year , . Therefore, . The slope is given by . Therefore, , which is equivalent to the equation in choice A.
Desmos solution:
Note: The regression uses t=0 and t=10 for the years after 2000, so its slope and intercept define P(t).
Enter in Desmos:
Reviewed and rewritten by CookSAT
Why the other choices are wrong
Choice B
Choice B is incorrect and may be the result of incorrectly calculating the slope as just the change in the value of .
Choice C
Choice C is incorrect and may be the result of the same error as in choice B, in addition to incorrectly using to represent the year, instead of the number of years after .
Choice D
Choice D is incorrect and may be the result of incorrectly using to represent the year instead of the number of years after .