SAT Question 1fe10d97: Nonlinear Functions answer and explanation with Desmos solution

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 $p\left(t\right)=90,000{\left(1.06\right)}^t$ yields $p\left(\frac{m}{12}\right)=90,000{\left(1.06\right)}^{\frac{m}{12}}$. Therefore, the function $r$ that best models the population of Lowell $m$ months after the census is $r\left(m\right)=90,000{\left(1.06\right)}^{\frac{m}{12}}$.