Answered: Test marketing for a new health-food… | bartleby

Trigonometry (MindTap Course List)

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section: Chapter Questions

Problem 33CT

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Question

Test marketing for a new health-food snack product in a selected area suggests that sales (inthousands of dollars) will increase at a rate given byS'(t)=40-40e-0.16t,t months after anaggressive national advertising campaign is begun. Find total sales during the second 12 months ofthe campaign. (Round to the nearest thousand dollars.

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The rate of U.S. per capita sales of bottled water for the period 2000–2010 can be approximated by s(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 fraction f(t) =√0.2 + 0.04t of 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 2008 to the start of 2010. HINT [Rate of consumption = s(t)f(t).] ____________ gal
The rate of U.S. per capita sales of bottled water for the period 2000–2010 can be approximated by s(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 fraction f(t) = 0.2 + 0.04t of 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 2004 to the start of 2010. HINT [Rate of consumption = s(t)f(t).]

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