Answer to Question #217967 in Algebra for Rashmay

Question

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

  P(t) = 14/1 +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) = P₀ e^kt , where P₀  is the initial population, would not be plausible?

Go to www.desmos.com/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 “÷” in the desmos 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)