The housing board of a newly planned town anticipates that over the next 12 years, 7,000 new residents will move in each year. In addition to the effect of new residents moving in, the board anticipates that each year the town’s population (i. e. whoever has been living there for the entirety of that year) will grow at an annual rate of 1.5%, due to the ordinary population changes resulting from births and deaths. Assume that whenever new residents move in they do so at the end of the year, and don’t start reproducing until the following year.

a. Why can this population growth scenario be considered an ordinary annuity?
b. What will the population be at the end of 12 years of such growth?
c. What if the town actually started out at the beginning of year 1 with 500,000 residents? What would be the population at the end of 12 years?

You are thinking of making your mansion more energy efficient by replacing some of the light bulbs with compact fluorescent bulbs, and insulating part or all of your exterior walls. each compact fluorescent light bulb costs $4 and saves you an average of $2 per year in energy costs, and each square foot of wall insulation costs $1 and saves you an average of $0.20 per year in energy costs.† your mansion has 150 light fittings and 3000 sq ft of uninsulated exterior wall. to impress your friends, you would like to spend as much as possible, but save no more than $750 per year in energy costs (you are proud of your large utility bills). how many compact fluorescent light bulbs and how many square feet of insulation should you purchase? how much will you save in energy costs per year? (if an answer does not exist, enter dne.)

When a shortage or a surplus arises in the loanable funds market a. the supply of loanable funds changes to return the economy to its original real interest rate b. the nominal interest rate is pulled to the new equilibrium level c. the demand for loanable funds changes to return the economy to its original real interest rate d. the real interest rate is pulled to the new equilibrium level

Imagine us is a startup that offers high definition 3d prenatal ultrasounds for high-end customers. the service process includes four activities that are conducted in the sequence described below. (the time required for each activity is shown in parentheses): activity 1: welcome a patient and explain the procedure. (20 minutes)activity 2: prep the patient (e. g., show them to the room, apply ultrasound gel). (17 minutes) (*your id number represents the amount of time needed to complete this task)activity 3: take images. (5 minutes)activity 4: discuss diagnostic with patient. (20 minutes)at each location there are employees (servers) s1, s2, and s3. the assignment of tasks to servers is the following: s1 does activities 1 and 2.s2 does activity 3.s3 does activity 4.a. what is the capacity of this process (in customers per hour)? b. suppose 3 patients arrive every hour on average. ignoring any “start of day” or “end of day” effects, what are the utilizations of all three servers (%)? c. suppose each activity can be done by any server and any server can do any set of activities. however, each activity is done by only one server. for example, a possible assignment includes: s1 does activity 1, s2 does activity 2, and s3 does activities 3 and 4. of course, the original assignment of servers to activities is also feasible. what is the maximum capacity of the process (in customers per hour)? d. now consider the capacity measures in (c) and (a), what is the percentage change? why can you improve capacity without using additional resources? (there is no free lunch, right? )note: for all hw assignments, show your process of getting the results. only providing the final answers is not acceptable and will get 0%. if necessary, use a separate sheet of paper to show your work.