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Choice B is correct. It’s given that the formula $P=C{\left(2\right)}^{rt}$ gives the number of bacteria in a growth medium, where $r$ and $C$ are constants and $P$ is the number of bacteria $t$ hours after the initial measurement. It’s also given that a scientist initially measures $\mathrm{12,000}$ bacteria in the growth medium. Since the initial measurement is $0$ hours after the initial measurement, it follows that when $t=0$, $P=\mathrm{12,000}$. Substituting $0$ for $t$ and $\mathrm{12,000}$ for $P$ in the given equation yields $\mathrm{12,000}=C{\left(2\right)}^{r\left(0\right)}$, or $\mathrm{12,000}=C{\left(2\right)}^0$, which is equivalent to $\mathrm{12,000}=C$.  It’s given that $4$ hours later, the scientist measures $\mathrm{24,000}$ bacteria, or when $t=4$, $P=\mathrm{24,000}$. Substituting $4$ for $t$, $\mathrm{24,000}$ for $P$, and $\mathrm{12,000}$ for $C$ in the given equation yields $\mathrm{24,000}=\mathrm{12,000}{\left(2\right)}^{4r}$. Dividing each side of this equation by $\mathrm{12,000}$ yields $2=2^{4r}$, or $2^1=2^{4r}$, which is equivalent to $1=4r$. Dividing both sides of this equation by $4$ yields $\frac{1}{4}=r$. Therefore, the value of $r$ is $\frac{1}{4}$.

Choice A is incorrect. This is the value of the reciprocal of $C$.

Choice C is incorrect. This is the value of the reciprocal of $r$.

Choice D is incorrect. This is the value of $C$.