The population will grow based on this model once a light source is provided and stop immediately once the light source is removed. P(t)=3et/4 Your computer continues with a note from the files that the alien civilization performed these calculations on the linearization of P(t) . Therefore, you will need to linearize P(t) and then use that model to determine when to remove the light source to have 3.09 million bacteria. Your linearization should be around t=0 , since this is the time when the light source is switched on.