SAT Question 3cf2698e: Nonlinear Functions answer and explanation with Desmos solution

Choice B is correct. For a bacteria with an initial population of $P$ cells and a doubling time of $m$ minutes, the number of cells, $f\left(x\right)$, of the bacteria $x$ minutes after the growth period begins can be given by the equation $f\left(x\right)=P{\left(2\right)}^{\frac{x}{m}}$. It’s given that there are $830$ cells of the bacteria when the growth period begins. Therefore, $P=830$. It’s also given that the number of cells of the bacteria doubles every $25$ minutes during the growth period. Therefore, $m=25$. Substituting $830$ for $P$ and $25$ for $m$ in the equation $f\left(x\right)=P{\left(2\right)}^{\frac{x}{m}}$ yields $f\left(x\right)=830{\left(2\right)}^{\frac{x}{25}}$.