Reminder Round all answers to two decimal places unless otherwise indicated.
Math and the City An article in The New York Times states, "The number of gas stations [in a city] grows only in proportion to the
a. If one city is twice as large as another, how do the numbers of gas stations compare?
b. The population of Houston, Texas, is
c. Los Angeles has a population of about
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Chapter 5 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Growth in Length of Haddock D.S. Raitt found that the length L of haddock in centimeters as a function of the age t in years is given approximately by the formula L=5342.820.82t a. Calculate L(4) and explain what it means. b. Compare the average yearly rate of growth in length from age 5 to age 10 years with the average yearly rate of growth from age 15 to age 20 years. Explain in practical terms what this tells you about the way haddock grow. c. What is the longest haddock you would expect to find anywhere?arrow_forwardPoverty The passage of the Social Security Amendments of 1965 resulted in the creation of the Medicare and Medicaid program. Since then, the percent of persons 65 years and over with family income below the poverty level has declined. The percent can be approximated by the following function: Pt=30.60-5.79lnt, Where t is the number of years since 1965. Find the percent of persons 65 years and over with family income below the poverty level and the rate of change in the following years. Source: U.S. Census. a. 1970 b. 1990 c. 2010 d. What happens to the rate of change over time?arrow_forwardGrowth in Weight and Height Between the ages of 7 and 11 years, the weight w, in pounds, of a certain girl is given by the formula w=8t. Here t represents her age in years. a. Use a formula to express the age t of the girl as a function of her weight w. b. At what age does she attain a weight of 68 pounds? c. The height h, in inches, of this girl during the same period is given by the formula h=1.8t+40. i. Use you answer to part b to determine how tall she is when she weighs 68 pounds. ii. Use a formula to express the height h of the girl as a function of her weight w. iii. Answer the question in part i again, this time using your answer to part ii.arrow_forward
- Whales Diving The figure on the next page, already shown in section 1.3 on a Properties of Functions, shows the depth of a sperm whale as a function of time, recorded by researches at the Woods Hole Oceanographic Institution in Massachusetts. Source: Peter Tyack, Woods Hole Oceanographic Institution. a. Find the rate that the whale was descending at the following times. i. 17 hours and 37 minutes ii. 17 hours and 39 minutes b. Sketch a graph of the rate the whale was descending as a function of time.arrow_forwardCortisone Concentration A mathematical model for the concentration of administered cortisone in humans over a 24 hour period uses the function C=DaV(ab)(ebteat) Where C is the concentration, D is the dose given at time t=0, V is the volume of distribution volume divided by bioavailability, a is the absorption rate, b is the elimination rate, and t is the time in hours. Source: Journal of Pharmacokinetics and Bio pharmaceutics. a. What is the value of C at t=0? Explain why this makes sense. b. What happens to the concentration as a large amount of time passes? Explain why this makes sense. c. The researchers used the values D=500micrograms,a=8.5,b=0.09 andV=3700liters. Use these values and a graphing calculator to estimate when the concentration is greatest.arrow_forwardAverage Price Otis Taylor plots the price per share of a stock that he owns as a function of time and finds that it can be approximated by the function S(t)=t(255t)+18 where t is the time in years since the stock was purchased. Find the average price of the stock over the first five years.arrow_forward
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