In this model,Pis the population of bacteria (total count, measured in millions) and tis the time measured in minutes. 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)=5e^{\frac{t}{8}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 5.155 million bacteria. Your linearization should be around t=0, since this is the time when the light source is switched on.

L(t)=

Using this linearization, after how many minutes (to three decimal places)will you turn off the light to generate a population of 5.155 million bacteria?

t= minutes