[b]Disclaimer: [/b]This problem came from an excellent calculus text, yet I couldn't find which one (since I have so many...) [br][br][b]Problem:[color=#1e84cc][br]A population of honeybees [/color]([/b][i]y[/i][b]) [/b]raised on a farm started with 50 bees at time [i]x[/i] = 0 and was modeled by the function [br][br][math]P\left(x\right)=\frac{75,200}{1+1503e^{-0.5932x}}[/math]. (exponent = -0.5932[i]x[/i] just in case you have a difficult time seeing it.) [br][br]In this problem, [i]x[/i] = time in weeks, for [math]0\le x\le25[/math]. [br][br][color=#1e84cc][b]The graph of function [i]P[/i] is shown in blue. [/b][/color][br][b][color=#9900ff]The graph of function [i]P' [/i]is shown in purple.[/color][/b] [br][br]Interact with this applet for a minute, then answer the questions that follow.