Aging Population The population of Americans age 55 and older as a percentage of the total population is approximated by the function f(t) = 10.72(0.9t + 10)0.3 (0 sts 20) where t is measured in years, with t = 0 corresponding to the year 2000.t At what rate was the percentage of Americans age 55 and older changing at the beginning of 2006? (Round your answer to four decimal places.) % per year At what rate was the percentage of Americans age 55 and older changing in 2020? (Round your answer to four decimal places.) % per year What was the percentage of the population of Americans age 55 and older in 2020? (See Note on page 168. Round your answer to two decimal places.) Need Help? Read It Watch it

Aging Population The population of Americans age 55 and older as a percentage of the total population is approximated by the function f(t) = 10.72(0.9t + 10)0.3 (0 sts 20) where t is measured in years, with t = 0 corresponding to the year 2000.t At what rate was the percentage of Americans age 55 and older changing at the beginning of 2006? (Round your answer to four decimal places.) % per year At what rate was the percentage of Americans age 55 and older changing in 2020? (Round your answer to four decimal places.) % per year What was the percentage of the population of Americans age 55 and older in 2020? (See Note on page 168. Round your answer to two decimal places.) Need Help? Read It Watch it

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Exponential And Logarithmic Functions

Section5.1: Exponential Functions And Their Graphs

Problem 61E: Population Growth The projected population of the United States for the years 2025 through 2055 can...

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Sales Growth In this exercise, we develop a model for the growth rate G, in thousands of dollars per year, in sales of the product as a function of the sales level s, in thousands of dollars. The model assumes that there is a limit to the total amount of sales that can be attained. In this situation, we use the term unattained sales for difference this limit and the current sales level. For example, if we expect sales grow to 3 thousand dollars in the long run, then 3-s is the unattained sales. The model states that the growth rate G is proportional to the product of the sales level s, and the unattained sales. Assume that the constant of proportionality is 0.3 and that the sales grow to 2 thousand dollars in the long run. a.Find the formula for unattained sales. b.Write an equation that shows the proportionality relation for G. c.On the basis of the equation from the part b, make a graph of G as a function of s. d.At what sales level is the growth rate as large as possible? e.What is the largest possible growth rate?
Arboriculture The growth of a red oak tree is approximated by the function G=0.003t3+0.137t2+0.458t0.839,2t34 where G is the height of the tree (in feet) and t is its age (in years). (a) Use a graphing utility to graph the function. (b) Estimate the age of the tree when it is growing most rapidly. This point is called the point of diminishing returns because the increase in size will be less with each additional year. (c) Using calculus, the point of diminishing returns can be found by finding the vertex of the parabola y=0.009t2+0.274t+0.458. Find the vertex of this parabola. (d) Compare your results from parts (b) and (c).
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?
Titanic At 2:00 p.m. on April 11, 1912, the Titanic left Cobh, Ireland, on her voyage to New York City. At 11:40 p.m. on April 14, the Titanic struck an iceberg and sank, having covered only about 2100 miles of the approximately 3400-mile trip. (a) What was the total duration of the voyage in hours? (b) What was the average speed in miles per hour? (c) Write a function relating the distance of the Titanic from New York City and the number of hours traveled. Find the domain and range of the function. (d) Graph the function in part (c).
Radioactive Decay The half-life of radium-226 is 1590 years. (a)If a sample has a mass of 150 mg, find a function that models the mass that remains after tyears. (b)Find the mass that will remain after 1000 years. (c)After how many years will only 50 mg remain?
Marine Fishery One class of models for population growth rates in marine fisheries assumes that the harvest from fishing is proportional to the population size. For one such model, we have G=0.3n(1n2)0.1n Here G is the growth rate of the population, in millions of tons of fish per year, and n is the population size, in millions of tons of fish. a.Make a graph of G versus n. include values of n up to 1.5 million tons. b.Use functional notation to express the growth rate if the population size is 0.24 million tons, and then calculate that value. c. Calculate G1.42 and explain in practical terms what your answer means. d.At what population size is the growth rate the largest?