The rate of change of the projected total assets (in constant 2005 dollars) in a government trust fund for the years 2000 through 2040 can be modeled as f(x) = -0.365x2 + -0.295x + 176.31 where output is measured in billion dollars per year and x is the number of years after 2000. Check: f(2)=174.26 (a) When will the trust fund assets be growing? When will they be declining? (Round your answers to the nearest integer.) The projected total assets in the trust fund are growing from the year 2000 through the year 2040 The projected total assets in the trust fund are declining from the year through the year (b) When will the amount in the trust fund be greatest? (Round your answer to three decimal places.) The amount in the trust fund will be at a maximum years after 2000. (c) Use a definite integral to find the total signed area between between f(x) and the x-axis from x=0 to x=35. (Round your answer to three decimal places.) Interpret the result. The amount in the trust fund is projected to ---Select--- by $ billion from the year 2000 to the year 2035. (d) What additional information would need to be known in order to calculate the amount projected to be in the trust fund in the year 2035? O In order to determine the projected amount in the trust fund in 2035, we would need to know the amount in the fund in the year 2000. O In order to determine the projected amount in the trust fund in 2035, we would need to know the rate of change of the projected total asse in the fund in the year 2000. O In order to determine the projected amount in the trust fund in 2035, we would need to know the rate of change of the projected total asse in the fund in the year 2035. O In order to determine the projected amount in the trust fund in 2035, we would need to know the rate of change of the projected total asse in the fund for the years 2000 through 2035.
The rate of change of the projected total assets (in constant 2005 dollars) in a government trust fund for the years 2000 through 2040 can be modeled as f(x) = -0.365x2 + -0.295x + 176.31 where output is measured in billion dollars per year and x is the number of years after 2000. Check: f(2)=174.26 (a) When will the trust fund assets be growing? When will they be declining? (Round your answers to the nearest integer.) The projected total assets in the trust fund are growing from the year 2000 through the year 2040 The projected total assets in the trust fund are declining from the year through the year (b) When will the amount in the trust fund be greatest? (Round your answer to three decimal places.) The amount in the trust fund will be at a maximum years after 2000. (c) Use a definite integral to find the total signed area between between f(x) and the x-axis from x=0 to x=35. (Round your answer to three decimal places.) Interpret the result. The amount in the trust fund is projected to ---Select--- by $ billion from the year 2000 to the year 2035. (d) What additional information would need to be known in order to calculate the amount projected to be in the trust fund in the year 2035? O In order to determine the projected amount in the trust fund in 2035, we would need to know the amount in the fund in the year 2000. O In order to determine the projected amount in the trust fund in 2035, we would need to know the rate of change of the projected total asse in the fund in the year 2000. O In order to determine the projected amount in the trust fund in 2035, we would need to know the rate of change of the projected total asse in the fund in the year 2035. O In order to determine the projected amount in the trust fund in 2035, we would need to know the rate of change of the projected total asse in the fund for the years 2000 through 2035.
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.3: Lines
Problem 92E
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Transcribed Image Text:The rate of change of the projected total assets (in constant 2005 dollars) in a government trust fund for the years 2000 through 2040 can be modeled as
f(x) = -0.365x² + -0.295x + 176.31
where output is measured in billion dollars per year and x is the number of years after 200o.
Check: f(2)=174.26
(a) When will the trust fund assets be growing? When will they be declining? (Round your answers to the nearest integer.)
The projected total assets in the trust fund are growing from the year 2000
through the year 2040
The projected total assets in the trust fund are declining from the year
through the year
(b) When will the amount in the trust fund be greatest? (Round your answer to three decimal places.)
The amount in the trust fund will be at a maximum
years after 2000.
(c) Use a definite integral to find the total signed area between between f(x) and the x-axis from x=0 to x=35. (Round your answer to three
decimal places.)
Interpret the result.
The amount in the trust fund is projected to ---Select---
| by $
billion from the year 2000 to the year 2035.
(d) What additional information would need to be known in order to calculate the amount projected to be in the trust fund in the year 2035?
O In order to determine the projected amount in the trust fund in 2035, we would need to know the amount in the fund in the year 2000.
O In order to determine the projected amount in the trust fund in 2035, we would need to know the rate of change of the projected total assets
in the fund in the year 2000.
O In order to determine the projected amount in the trust fund in 2035, we would need to know the rate of change of the projected total assets
in the fund in the year 2035.
O In order to determine the projected amount in the trust fund in 2035, we would need to know the rate of change of the projected total assets
in the fund for the years 2000 through 2035.
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