Part 2: For many properties, frontage is an important attribute of property. For example, the lot pictured above has 200 feet of frontage. For commercial property, visibility and accessibility are important, so frontage makes a property more valuable. In such a situation, the front 50 feet of the lot should be worth more than the rear 50 feet of the lot. In the same way, the front 25 feet should be worth more than the second 25 feet of the lot, and so on. A method for finding the value of such a lot is to use what we call a worth function, w(x). The worth function, w(x), is defined as the value of a square foot of land whose center is x feet from the highway. Answer all of the following questions (for a 200 foot by 100 foot lot with 200 feet of frontage) for both of the worth functions: (1) w(x) = $(50 - 0.30x) per square foot, and (ii) w(x) = $(50e-0.30*) per square foot. 1. Compute the area of the lot. 2. What is the tax value of the lot? 3. What is the average tax value per square foot of the lot? 4. Find the value of the first x feet in terms of x. 5. Find the percentage of the value of the entire lot that is due to the first x in terms of x. 6. Graph pf(x) for x in 10, 100). 7. What value of x should you choose in order to divide the lot into two lots of equal tax value? 8. For a worth function w(x) = $(A + Bx) per square foot, what values of A and B make sense, and what will happen to the fair division point as A and B change