The following graph shows the approximate value of the U.S. Consumer Price Index (CPI) from September 2004 through November 2005. On the graph titled "CPI Sep 2004-Nov 2005," the horizontal axis is labeled t and the vertical axis is labeled I(t). The curve begins at the point (0, 190), goes up and right becoming more steep, passes through the approximate point (8, 195), goes up and right becoming less steep, and ends at the approximate point (14, 199.9). The approximating curve shown on the figure is given by I(t) = −0.005t3 + 0.12t2 − 0.01t + 190 (0 ≤ t ≤ 14), where t is time in months since the start of September 2004. (a) Use the model to estimate the monthly inflation rate in July 2005 (t = 10). Recall that the inflation rate is I′(t) I(t). (Round your answer to three decimal places.) % (b) Was inflation slowing or speeding up in July 2005? slowing downspeeding up (c) When was inflation speeding up? When was inflation slowing? (Use the model to determine this.) Inflation was speeding up prior to 2005 and slowing after 2005.
The following graph shows the approximate value of the U.S. Consumer Price Index (CPI) from September 2004 through November 2005. On the graph titled "CPI Sep 2004-Nov 2005," the horizontal axis is labeled t and the vertical axis is labeled I(t). The curve begins at the point (0, 190), goes up and right becoming more steep, passes through the approximate point (8, 195), goes up and right becoming less steep, and ends at the approximate point (14, 199.9). The approximating curve shown on the figure is given by I(t) = −0.005t3 + 0.12t2 − 0.01t + 190 (0 ≤ t ≤ 14), where t is time in months since the start of September 2004. (a) Use the model to estimate the monthly inflation rate in July 2005 (t = 10). Recall that the inflation rate is I′(t) I(t). (Round your answer to three decimal places.) % (b) Was inflation slowing or speeding up in July 2005? slowing downspeeding up (c) When was inflation speeding up? When was inflation slowing? (Use the model to determine this.) Inflation was speeding up prior to 2005 and slowing after 2005.
Chapter1: Equations, Inequalities, And Mathematical Modeling
Section1.1: Graphs Of Equations
Problem 9ECP
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The following graph shows the approximate value of the U.S. Consumer Price Index (CPI) from September 2004 through November 2005.
On the graph titled "CPI Sep 2004-Nov 2005," the horizontal axis is labeled t and the vertical axis is labeled I(t). The curve begins at the point (0, 190), goes up and right becoming more steep, passes through the approximate point (8, 195), goes up and right becoming less steep, and ends at the approximate point (14, 199.9).
The approximating curve shown on the figure is given by
I(t) = −0.005t3 + 0.12t2 − 0.01t + 190 (0 ≤ t ≤ 14),
where t is time in months since the start of September 2004.
(a)
Use the model to estimate the monthly inflation rate in July 2005 (t = 10).
Recall
that the inflation rate is
.
(Round your answer to three decimal places.)
| I′(t) |
| I(t) |
%
(b)
Was inflation slowing or speeding up in July 2005?
slowing downspeeding up
(c)
When was inflation speeding up? When was inflation slowing? (Use the model to determine this.)
Inflation was speeding up prior to 2005 and slowing after 2005.
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