Explanation
Correct answer: D.
Choice D is correct. Stating that the population will increase each year by from the previous year is equivalent to saying that the population each year will be of the population the year before. Since the initial population is , the population after years is given by . It follows that the equation can be used to estimate the number of years it will take for the population to reach .
Desmos solution:
Note: The line P(t)=50000*(1.03)^t models the population after t years. Check that when t=0 the output is 50000, and that the value reaches 60000 between t=6 and t=7, matching choice D.
Enter in Desmos:
Reviewed and rewritten by CookSAT
Why the other choices are wrong
Choice A
Choice A is incorrect. This equation models how long it will take the population to decrease from to , which is impossible given the growth factor.
Choice B
Choice B is incorrect and may result from misinterpreting a growth as growth by a factor of . Additionally, this equation attempts to model how long it will take the population to decrease from to .
Choice C
Choice C is incorrect and may result from misunderstanding how to model percent growth by multiplying the initial amount by a factor greater than .