A scientist initially measures $\mathrm{12,000}$ bacteria in a growth medium. $4$ hours later, the scientist measures $\mathrm{24,000}$ bacteria. Assuming exponential growth, the formula $P=C{\left(2\right)}^{rt}$ gives the number of bacteria in the growth medium, where $r$ and $C$ are constants and $P$ is the number of bacteria $t$ hours after the initial measurement. What is the value of $r$?