MAT 117- Problem Set 2 Objective B1. An adventurer has reached the top of a mountain, which is 14,982 feet above sea level. After resting, the adventurer begins climbing down the mountain. Four days later, the adventurer reaches the height of 9,675 feet above sea level.a. [2 pts] Determine the average rate of change (slope) of the adventurerβs height above sea level with respect to the time spent climbing down the mountain. b. [2 pts] If π₯ is the number of days since the adventurer began her descent and π(π₯) is the number of feet the adventurer is above sea level, find the equation of the line through these two points.c. [2 pts] Assuming π(π₯) is a linear function, use the equation to predict the height of the adventurer above sea level after six days since descending from the summit of the mountain.2. Michelle asks her husband to build a pen for her chickens. Three of the sides will be built with mesh fencing, while the fourth side will back up to the east side of her house. She wants the enclosed area to be 400 square feet. The cost of the fence meshing will be $4.18 per foot and the pen will also need 4 corner posts costing $9.50 each.a. [6 pts] Let π₯ be the length of the side of the chicken coop that backs up to the east side of the house. Write a function π(π₯), for the price of the materials for the pen in terms of x. Simplify your answer.b. [3 pts] Use your calculator to find the dimensions of the pen that costs the least. Set your window with: 0 β€π₯β€80 and 10 β€π¦β€400, and round your answer to 2 decimal places. (Insert your graph here. You may hand draw the graph or insert an image of the graph from Desmos)c. [1 pt] What is the total cost of the pen? Round to dollars and cents.3. Consider the piecewise defined function f:π(π₯) = {0.75π₯β0.25 β4 β€π₯< 24 2 β€π₯< 4β0.54π₯ 2 4 β€π₯β€6a. [3 pts] Graph the π(π₯). (Insert your graph here. You may hand draw the graph or insert an image of the graph from Desmos)b. [2 pts] Write the domain of π using interval notationc. [2 pts] Write the range of π using interval notationd. [2 pts] On what interval(s) is π(π₯) decreasing?