This activity requires you to do some research about building a house. As you conduct this research, you will determine the best function to use for some of the steps. You will also have to determine which information will be important to your task and which information is less important or even irrelevant. Step 1 You have purchased land that is 200 ft. wide by 600 ft. long. In your area, the footprint of a house is allowed to take up 13 of the total area of a lot, and you want your house centered on the lot. Given these constraints, what is the largest area you can have for your house? Include the length and width dimensions. Step 2 Determine how much it will cost to build your house. Use the internet to research the costs of building materials and labor in your area per square foot. You determined the area of the ground floor in Step 1, but will your house have a second floor? Or a finished basement? The number of bedrooms and bathrooms can also increase the building costs. Create a function to model the total costs for your house. Then create a graph to model the function. Step 3 Once your house is built, how much will you pay for it? Many people have to take out a mortgage, which earns compound interest over the time of the loan. Research home loans online to find out the current interest rates and length of loans. Determine how many times the interest will be compounded. What will your monthly mortgage payment be? What type of function is this?

Question

Answer each question in 2-3 sentences
write it like a 9th grader would

Answer 1

Step 1:

To find the largest area for the house, we first calculate the total area of the lot, which is 200 ft × 600 ft = 120,000 sq ft. Since the house can take up 13% of that area, the maximum area for the house would be 0.13 × 120,000 sq ft = 15,600 sq ft. To center the house, we could make it approximately 120 ft wide and 130 ft long because 120 ft × 130 ft equals 15,600 sq ft.

Step 2:

Next, we need to figure out the cost to build the house. Let’s say it costs around $150 per square foot in my area. If the house is 15,600 sq ft, the cost would be 15,600 sq ft × $150/sq ft = $2,340,000. The function for the total cost could look something like \( C(x) = 150x \) where \( x \) is the area in square feet. I could make a graph of this function to show how the cost increases with more area.

Step 3:

To find out how much I'll pay monthly for the house, I’ll need to get a mortgage. If I take out a loan for $2,340,000 at an interest rate of about 4% for 30 years, I would need to determine how often the interest is compounded. For most mortgages, it’s compounded monthly. The function for the monthly mortgage payment is an exponential function, and I could use the formula for calculating mortgage payments to get the monthly amount. This might cost around $11,158 each month, but it can vary based on different factors.