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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
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Exponential And Logarithmic Functions
Section: Chapter Questions
Problem 37CT: On the day a grandchild is born, a grandparent deposits $2500 in a fund earning 7.5% interest,...
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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    
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