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

p(t)= {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 p(t)=p_0 \ e^{kt} , where p_0 is the initial population, would not be plausible? what are the virtues of the logistic model?

go to calculator and 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 “\div” in the calculator after selecting “14250”, or you type “/” after selecting “14250”, and you will also find the function “exp” ). adjust the x and y axes 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.