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 · 2t − 3t ) = 400 · 2t − 100 · 3t .
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