The rate of U.S. per capita sales of bottled water for the period 2000-2010 can be approximated bys(t) = −0.18t² + 3t + 15 gallons per year (0 ≤ t ≤ 10),where t is the time in years since the start of 2000.† After conducting a survey of sales in your state, you estimate that consumption in gyms accounts for a fractionf(t) = √0.2 + 0.04tof all bottled water consumed in year t. Assuming that your model is correct, estimate, to the nearest gallon, the total amount of bottled water consumed per capita in gyms from the start of 2005 to the start of 2010. HINT[Rate of consumptions(t)f(t).]=gal

The solution is shown in step-2

Answered: The rate of U.S. per capita sales of…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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According to the U.S. Census Bureau, the population of the United States in 2008 was 304 million people. In addition, the population of the United States was growing at a rate of 1.1% per year. Assuming this growth rate continues, the model P(t) = 304 · (1.011)* - represents the population P (in millions of people) in year t. According to the model, when will the population be 407 million people? Be sure to round your answer to the nearest whole year. Year
Data about the sound levels from a new speaker are collected at a manufacturing facility and are used to calculate the model ŷ = 62.4(0.915)x, where x represents the distance from the speaker in meters and ŷ represents the predicted sound level in decibels. Interpret the percent rate of change of the model in the context of the problem. For every increase in one meter from the speaker, the sound level is predicted to decrease by about 91.5%. For every increase in one meter from the speaker, the sound level is predicted to decrease by about 8.5%. For every increase in one meter from the speaker, the sound level is predicted to increase by about 91.5%. For every increase in one meter from the speaker, the sound level is predicted to increase by about 8.5%.
In 2010, the population of a country was 53 million and growing at a rate of 1.7% per year. Assuming the percentage growth rate remains constant, express the population, P, in millions, as a function of t, the number of years after 2010. P = f(t) = [ million people help (formulas)
2. Lijah opened an account at Advantis Credit Union. The balance of her account after x years is represented by the function b(x) = 500(1.05)*. What annual interest rate is Lijah earning? а. b. After how many years did it take for Lijah's balance to double? Show all of your work.
According to the U.S. Census Bureau, the population of the United States in 2008 was 304 million people. In addition, the population of the United States was growing at a rate of 1.1% per year. Assuming this growth rate continues, the model t – 2008 P(t) = 304 · (1.011)* represents the population P (in millions of people) in year t. According to the model, when will the population be 366 million people? Be sure to round your answer to the nearest whole year. Year

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