sat-dog

Choice D is correct. It's given that a model predicts the population of Springfield in $2005$ was $\mathrm{15,000}$. The model also predicts that each year for the next $5$ years, the population increased by $4\%$ of the previous year's population. The predicted population in one of these years can be found by multiplying the predicted population from the previous year by $1.04$. Since the predicted population in $2005$ was $\mathrm{15,000}$, the predicted population $1$ year later is $\mathrm{15,000}\left(1.04\right)$. The predicted population $2$ years later is this value times $1.04$, which is $\mathrm{15,000}\left(1.04\right)\left(1.04\right)$, or $\mathrm{15,000}{\left(1.04\right)}^2$. The predicted population $3$ years later is this value times $1.04$, or $\mathrm{15,000}{\left(1.04\right)}^3$. More generally, the predicted population, $p$, $x$ years after $2005$ is represented by the equation $p=\mathrm{15,000}{\left(1.04\right)}^x$. 

Choice A is incorrect. Substituting $0$ for $x$ in this equation indicates the predicted population in $2005$ was $0.96$ rather than $\mathrm{15,000}$.

Choice B is incorrect. Substituting $0$ for $x$ in this equation indicates the predicted population in $2005$ was $1.04$ rather than $\mathrm{15,000}$.

Choice C is incorrect. This equation indicates the predicted population is decreasing, rather than increasing, by $4\%$ each year.