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Honeybee Population (Growth Rate Question)

Disclaimer: This problem came from an excellent calculus text, yet I couldn't find which one (since I have so many...) Problem: A population of honeybees (y) raised on a farm started with 50 bees at time x = 0 and was modeled by the function . (exponent = -0.5932x just in case you have a difficult time seeing it.) In this problem, x = time in weeks, for . The graph of function P is shown in blue. The graph of function P' is shown in purple. Interact with this applet for a minute, then answer the questions that follow.


What are the units of the y-coordinate of the PINK POINT?


What are the units of the y-coordinate of the GREEN POINT? (Why is this?)


Use calculus to algebraically determine the time at which the bee population was increasing at the fastest rate. Then use the applet to estimate the value of this fastest growth rate.

Quick (Silent) Demo