A population of bacteria is growing according to the equation

Question

A population of bacteria is growing according to the equation P(t)=300e^0.19t. Estimate when the population will exceed 492.

t=

Answer 1

First, let's set the equation of P(t) to the given value of 492:

P(t) = 300e^0.19t = 492

Now, let's solve for t and we'll have our answer:

e^0.19t = 492/300

ln(e^0.19t) = ln(492/300)

0.19t = ln(492/300)

t = ln(492/300)/0.19

t = 2.604