First, work through the questions on the following pages. But think of filling out this handout as a rough draft! You should write up your solutions as a typed or very neatly handwritten report for your final product. If you type, use Word or GoogleDocs, and use the equation editor to type math. You can also make tables in Word and GoogleDocs. And if your solution includes graphs or pictures, you can take screenshots and include them as images. Please feel free to ask for help! For each of the two problems in this project, follow these guidelines for your report: ? Introduce the problem first. You may paraphrase the problem statement. A reader should be able to follow your document without having to refer to the original handout. ? Try to write your report less as a sequence of questions & answers, and more as a narrative. ? Write in complete sentences! You can center important equations, but they should still be part of your narrative flow. ? Write as if you were explaining the solution to another Math 121 student who hasn't seen the project yet. Your solution should be organized and have enough detail so that the reader can easily follow it.

2. A hiker starting at a point P on a straight road walks east towards point O, which is on the road and 3 kilometers from point P. Two kilometers due north of point Q is a cabin. The hiker will walk down the road for a while, at a pace of 8 kilometers per hour. At some point Z between P and Q, the hiker leaves the road and makes a straight line towards the cabin through the woods, hiking at a pace of 3 kph. In order to minimize the time to go from P to Z to the cabin, where should the hiker tum into the forest? cabin If you like, use the following checklist to help you solve the problem: (a) Assign variables to the quantities in the diagram above that can change. (Hint: What points are i'ixed'.7 W'hat points are movable?) (b) Use your variabl$ to write an expmsion for the distance the hiker will travel. (0) Then write an expression for the total time it will take the hiker to travel this distance. (Hint: How are distance, time, and speed related? It may be helpful to make sure your units work out correctly.) (d) If you don't already have total time written as a function of a single variable, use the diagram and your math knowledge to eliminate extra variables. (e) Identify what interval your total time function makes sense on. (f) Use the appropriate methods from this unit to nd the absolute minimum of the time function on the interval you found. (g) Write a sentence answering the qu$tion asked in the original problem state- ment, remembering to include units where appropriate