Exponential Population Growth Model

In a certain town, the population $P$ increases according to the exponential model given by the equation:

$$P(t) = P_0 e^{rt}$$

where:

• $P_0$ is the initial population,
• $r$ is the rate of growth, and
• $t$ is the time in years.

Suppose the initial population of the town is at 5,000 residents, and the annual population growth rate is 4%. After how many years will the population reach at least 10,000 residents?