Modeling with Mathematics

Question

The life zones on Mount Rainier, a mountain in Washington, can be approximately classified by elevation, as follows.

Low elevation forest: above 1700 feet to 2500 feet

Mid elevation forest: above 2500 feet to 4000 feet

Subalpine: above 4000 feet to 6500 feet

Alpine: above 6500 feet to the summit

Elevation of Mount Rainer: 14,410 ft

Wkrte a compound inequality that represents the elevation range for each type of plant life.

part a.) trees in the low- elevation forest zone

part b.) flowers in the subalpine and alpine zones

Answer 1

It's been a little while since I've looked at compound inequalities, so forgive me if this is a bit long.

Let's start with the Low Elevation Forest. Let x represent what is considered the forest. If this is above 1700, x>1700 (which can be rewritten as 1700<x). (Remember, as silly as this may sound, the mouth of the aligator eats the larger part! So the large number has the wide part of the symbol. Remember also that if the sign is < or >, then it includes the number the 'mouth' is facing.) If the forest is up to 2500, you'll generally include 2500 in your equation, so x<2500. This means 1700<x<2500 or x>1700 and x<2500.

Now let's repeat that with the other parts of the question. Mid elevation is x>2500 and x<4000. Subalpine would be x>4000 and x<6500. Alpine is then x>6500 and x< the summit (which is probably the elevation of Mount Rainer in this problem or 14410 feet).

Now we have the question itself. Let's replace x with t for trees for part a. This would mean in the low elevation forest, t>1700 and t<2500 which can be rewritten 1700<t<2500. Now we have flowers in the subalpine AND alpine zones. Let's use f for flowers. If flowers can be in either zone, let's combine them! Because t>4000 and t<6500 in the subalpine level and t>6500 and < the summit (aka 14410 feet), flowers can grow anywhere above 4000 feet. So flowers would be f>4000 and f<14410. Again, you can combine these into: 400<f<14410.

I hope that helped!