# The population of a culture of bacteria is modeled by the logistic equation

The population of a culture of bacteria is modeled by the logistic equationP (t ) =14,2501+29e-0.62tTo the nearest tenth, how many days will it take the culture to reach 75% of its carrying capacity? What is the carryingcapacity? What is the initial population for the model? Why a model like P(t) = Po ekt, where Po is the initialpopulation, would not be plausible? What are the virtues of the logistic model?Go to www.desmos.com/calculator and typey = 14250 / (1 + 29 . e-0.62x). {0 < x < 15} {0 < y < 15000}y = 14300 {0 < x < 15}(you will find the command ":"in the desmos calculator after selecting "14250", or you type "/" after selecting "14250", andyou will also find the function "exp" ). Adjust the x and y axes settings to 0 < x < 15 and 0 < y < 15000. Plot the graph youhave obtained (you can use a screenshot, save as image, and copy it into word). If you need, or if you want, go to the CourseForum and tell us something about this plotting task.