Choice D is correct. The student first recognizes that a population that doubles in size over equal time periods is increasing at an exponential rate. An exponential growth model can be written in the form y equals

a((2)^(x/b)) where a is the population at time 0, since 2 raised to the zeroth power is 1 and b is the doubling time, since when x =12 ,

2 is raised to the first power, and the population will be (2^1) * a =2a.

From the way the variables were defined, the population at time n =0 is 50 and the doubling time is 12.

Choice A is not the correct answer. This answer may result from a misunderstanding of exponential equations or of the context. A student who tries to model the scenario with a linear equation or who misunderstands that the y-intercept of a linear model should represent the initial number of animals may produce this equation.

Choice B is not the correct answer. This answer may result from a misunderstanding of exponential equations or of the scenario. A student who tries to model the scenario with a linear equation may produce this equation.

Choice C is not the correct answer. A student who tries to produce an exponential model, but does not understand how the 12 years affects the model, may incorrectly write the exponent.