### Home > CALC > Chapter 6 > Lesson 6.2.2 > Problem 6-76

The good news for the small prairie town of Woisme is that a new fiber optics plant is about to open. The bad news is that the old quarry is about to close, and many residents will lose their jobs as a result. The population is predicted to follow this model over the next few years: Homework Help ✎

*p*(*t*) = 100(4 · 2− 3^{t}) = 400 · 2^{t}^{t}^{ }− 100 · 3^{t}^{ }.Using complete sentences, relate the equation for

*p*(*t*) to the changes of industry.Algebraically determine when Woisme will have the most people. Use your calculator only for numerical calculations.

There are both positive and negative components to *p*(*t*). What do you think these components correspond to?

Find *p*'(*t*) and determine when *p*'(*t*) = 0.

Be sure to consider the endpoints. For example, Woisme's population might have been the greatest at the *t* = 0.

≈ 2.283 years