At the beginning of a study, a certain culture of bacteria has a population of 40. The population grows according to a continuous exponential growth model. After 6 days, there are 124 bacteria.

Answer 1

A=Pe^rt is the general formula for continuous growth or decay

A=Pe^6r

124=40e^6r

124/40=

3.1= e^6r

take natural logs of both sides

then divide by 6, solve for r

(ln3.1)/6=r

r=about .1886= 18.86% per day = the daily growth rate= rate of change

A=40e^[ln(3.1/6)t]

A= about 40e^.19t

where t = time measured in days, A =Amount after t days