15) Annual U.S. imports from a certain country in the years 1996 through 2005 could be approximated by I(t) = t2 + 3.5t + 48 (1 ≤ t ≤ 9) billion dollars, where t represents time in years since 1995. Annual U.S. exports to the country in the same years could be approximated by E(t) = 0.5t2 − 1.4t + 13 (0 ≤ t ≤ 10) billion dollars. Assuming that the trends shown in the above models continue indefinitely, calculate the limits lim t→+∞ I(t) and lim t→+∞ I(t)/E(t) algebraically. (If an answer does not exist, enter DNE.) lim t→+∞ I(t) = lim t→+∞ I(t) E(t) = Interpret your answers. In the long term, U.S. imports from the other country will (select) (be rounded or rise without bound) and be times U.S. exports to the other country. Could the given models be extrapolated far into the future? Yes or No
15) Annual U.S. imports from a certain country in the years 1996 through 2005 could be approximated by I(t) = t2 + 3.5t + 48 (1 ≤ t ≤ 9) billion dollars, where t represents time in years since 1995. Annual U.S. exports to the country in the same years could be approximated by E(t) = 0.5t2 − 1.4t + 13 (0 ≤ t ≤ 10) billion dollars. Assuming that the trends shown in the above models continue indefinitely, calculate the limits lim t→+∞ I(t) and lim t→+∞ I(t)/E(t) algebraically. (If an answer does not exist, enter DNE.) lim t→+∞ I(t) = lim t→+∞ I(t) E(t) = Interpret your answers. In the long term, U.S. imports from the other country will (select) (be rounded or rise without bound) and be times U.S. exports to the other country. Could the given models be extrapolated far into the future? Yes or No
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.3: Linear Functions And Slope
Problem 106E
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Question
15)
Annual U.S. imports from a certain country in the years 1996 through 2005 could be approximated by
I(t) = t2 + 3.5t + 48 (1 ≤ t ≤ 9)
billion dollars, where t represents time in years since 1995. Annual U.S. exports to the country in the same years could be approximated by
E(t) = 0.5t2 − 1.4t + 13 (0 ≤ t ≤ 10)
billion dollars.
Assuming that the trends shown in the above models continue indefinitely, calculate the limits
lim t→+∞ I(t)
and
lim t→+∞ I(t)/E(t)
algebraically. (If an answer does not exist, enter DNE.)
| lim t→+∞ I(t) | = |
|
||
lim t→+∞
|
= |
|
Interpret your answers.
In the long term, U.S. imports from the other country will (select) (be rounded or rise without bound) and be times U.S. exports to the other country.
Could the given models be extrapolated far into the future?
Yes or No
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