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

P(t)= \frac{14,250}{1+29e^{-0.62t}.

To the nearest tenth, how many days will it take the culture to reach 75% of its carrying capacity? What is the carrying capacity? What is the initial population for the model? Why a model like, whereis the initial population, would not be plausible? What are the virtues of the logistic model?

Go towww.desmos.com/calculatorand type

y = 14250 / (1 + 29 . e^{-0.62 x}).{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", and you will also find the function "exp" ). Adjust thexandyaxes settings to 0 < x < 15 and 0 < y < 15000. Plot the graph you have obtained (you can use a screenshot, save as image, and copy it into word). If you need, or if you want, go to the Course Forum and tell us something about this plotting task.