Concept explainers
Effect of Mortgage Rates on Housing Starts A study prepared for the National Association of Realtors estimated that the number of housing stalls per year over the next 5 years will be
million units, where r (percent) is the mortgage rate. Suppose the mortgage rate t months from now will be
percent/year.
- a. Find an expression for the number of housing starts per year as a function of t, t months from now.
- b. Using the result from part (a), determine the number of housing starts at present, 12 months from now. and 18 months from now.
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Chapter 2 Solutions
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
- Water Flea F. E Smith has reported on population growth of the water flea. In one experiment, he found that the time t, in days, required to reach a population of N is given by the relation e0.44t=NN0(228N0228N)4.46. Here N0 is the initial population size. If the initial population size is 50, how long is required for the population to grow to 125?arrow_forwardContinued This is a continuation of Exercise 13. As we saw earlier, the stock turnover rate of an item is the number of times that the average inventory of the item needs to be replaced as a result of sales in a given time period. Suppose that a hardware store sells 80 shovels each year. a. Suppose that the hardware store maintains an average inventory of 5 shovels. What is the annual stock turnover rate for the shovels? How is this related to the yearly number of orders to the wholesaler needed to restock inventory? b. What would he the annual stock turnover rate if the store maintained an average inventory of 20 shovels? c. Write a formula expressing the annual stock turnover rate as a function of the average inventory of shovels, identify the function and the variable, and state the units.arrow_forwardEconomic Efficiency Marginal cost is the additional cost imposed by the production of one additional item. Marginal benefit is the additional benefit of producing one additional item. For a certain company, the marginal cost C, in dollars, if it is currently producing n items, is given by C(n)=5+n, and the marginal benefit B, in dollars, is given by B(n)=250.9n. Economic efficiency occurs at the production level where marginal cost and marginal benefit are the same. What production level n gives economic efficiency for this company? Round the function values to one decimal place.arrow_forward
- Home Equity When you purchase a home by securing a mortgage, the total paid toward the principle is your equity in the home. If your mortgage is for P dollars, and if the term of the mortgage is t months, then your equity E in dollars, after k monthly payments is given by E=P(1+r)k1(1+r)t1 Here r is the monthly interest rate as a decimal, with r=APR/12 Suppose you have a mortgage of 425,000 at an APR of 9% and a term of 30 years. How long does it take for your equity to reach half of the amount of the original mortgage? Round r to four decimal places.arrow_forwardAn Uncertain Investment Suppose you invested 1300 in the stock market two years ago. During the first year the value of the stock increased by 12%. During the second year, the value of the stock decreased by 12%. How much money is your investment worth at the end of the two-year period? Did you earn money or lose money? Note: The answer to the first question is not 1300arrow_forwardDecomposing Functions To join a book club, you pay an initial fee and then a fixed price each month for a book. The total cost in dollars of joining the club and buying n books is given by C=30+17n. What is the initial fee? What is the cost of each book after you are a club member?arrow_forward
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