SAT Question 7ba694f3: Nonlinear Functions answer and explanation with Desmos solution

Choice D is correct. Since the number of bacteria doubles every day, the relationship between $t$ and $y$ can be represented by an exponential equation of the form $y=a{\left(b\right)}^t$, where $a$ is the number of bacteria at the start of the observation and the number of bacteria increases by a factor of $b$ every day. It's given that there are $44,000$ bacteria at the start of the observation. Therefore, $a=44,000$. It's also given that the number of bacteria doubles, or increases by a factor of $2$, every day. Therefore, $b=2$. Substituting $44,000$ for $a$ and $2$ for $b$ in the equation $y=a{\left(b\right)}^t$ yields $y=44,000{\left(2\right)}^t$.