# Honeybee Population (Growth Rate Question)

- Author:
- Tim Brzezinski

**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 = -0.5932

*x*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**Interact with this applet for a minute, then answer the questions that follow.

*P'*is shown in purple.## 1.

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

## 2.

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

## 3.

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**.