The population of a certain bacteria culture is modeled by the function $P(t)=P_0\cdot (1+r{)}^t$, where $P_0$ is the initial population, $r$ is the growth rate per hour, and $t$ is the time in hours. If the population triples every $5$ hours, and the initial population is $1,000$, what is the population after $7.5$ hours?