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Reminder Round all answer to two decimal places unless otherwise indicated.
Hair Growth When you are
a. Find a formula that gives
b. How long will it take for the hair to reach a length of
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Functions And Change A Modeling Approach To College Algebra
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- Physician Demand The demand for physicians is expected to increase in the future, as shown in the accompanying table. Source: Association of American Medical Colleges. Year Demand for Physicians in thousands 2006 680.5 2015 758.6 2020 805.8 2025 859.3 a. Plot the data, letting t=0 correspond to 2000. Does fitting an exponential curve to the data seem reasonable? b. Use the data for 2006 and 2015, to find the function of the form f(t)=Cekt that goes through these two points. c. Use your function from part b to predict the demand for physicians in 2020 and 2025. How well do these predictions fit the data? d. If you have graphing calculator or computer program with an exponential regression feature, use it to find an exponential function that approximately fits the data. How does this answer compare with answer to part b?arrow_forwardImmigration The following graph shows immigrationin thousand to the United States has varied over the past century. Source: Homeland Security. a. Find the average annual rate of change in immigration for the first half of the century from 1905 to 1955. b. Find the average annual rate of change in immigration for the second half of the century from 1955 to 2005. c. Find the average annual rate of change in immigration for the entire century from 1905 to 2005. d. Average your answers to part a and b, and compare the result with your answer from part c. Will these always be equal for any two time periods? e. If the annual average rate of change for entire century continues, predict the number of immigrants in 2009. Compare answer to the actual number of 1,130,818 immigrants.arrow_forwardGrowth 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_forward
- LIFE SCIENCE APPLICATIONS Brain Mass The brain mass of a fetus can be estimated using the total mass of the fetus by the function b=0.22m0.87, where m is the mass of the fetus in grams and b is the brain mass in grams. Suppose the brain mass of a 25-g fetus is changing at a rate of 0.25gperday. Use this to estimate the rate of change of the total mass of the fetus, dm/dt. Source: Archives dAnatomie, d Histologie et d Embryologie.arrow_forwardThe half-life of plutonium-244 is 80,000,000 years. Find function gives the amount of carbon-14 remaining as a function of time, measured in years.arrow_forwardLIFE SCIENCE APPLICATIONS Population GrowthThe rate of change of the population of a rare species of Australian spider for one year is given by f(t)=100t0.4t2+1, where f(t) is the number of spiders present at time t in months. Find the total number of additional spiders in the first 10 months.arrow_forward
- LIFE SCIENCE APPLICATIONS Growth of a Population The rate of growth of a microbe population is given by m(t)=27te3t Where t is time in days. What is the total accumulated growth during the first 2 days?arrow_forwardFlood Control A river is 8 feet above its flood stage. The water is receding at a rate of 3 inches per hour. Write a mathematical model that shows the number of feet above flood stage after t hours. Assuming the water continually recedes at this rate, when will the river be 1 foot above its flood stage?arrow_forwardLIFE SCIENCE APPLICATIONS APPLY IT Rate of growth The area covered by a patch of moss is growing at a rate of A(t)=tlnt cm2 per day, for t1. Find the additional amount of area covered by the moss between 4 and 9 days.arrow_forward
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