Nonlinear functions SAT question

Choice D is correct. It’s given that the function $p$ models the population of Lowell $t$ years after a census. Since there are $12$ months in a year, $m$ months after the census is equivalent to $\frac{m}{12}$ years after the census. Substituting $\frac{m}{12}$ for $t$ in the equation $p(t)=90,000{(1.06)}^t$ yields $p(\frac{m}{12})=90,000{(1.06)}^{\frac{m}{12}}$. Therefore, the function $r$ that best models the population of Lowell $m$ months after the census is $r(m)=90,000{(1.06)}^{\frac{m}{12}}$.

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 C is incorrect and may result from conceptual or calculation errors.