Question

Annual U.S. imports from a certain country in the years 1996 through 2003 can be approximated by

I(t) = t^2 + 3.7t + 50 (1 leq t leq 9)
billion dollars, where t represents time in years since 1995. Annual U.S. exports to this country in the same years can be approximated by
E(t) = 0.3t^2-1.4t + 16 (0 leq t leq 10)
billion dollars.
Assuming the trends shown in the above models continue indefinitely, numerically estimate the following. (If you need to use infinite or -infinite, enter INFINITY or -INFINITY, respectively. If an answer does not exist, enter DNE.)
lim t tends to +infinite and
lim t tends to +infinite E(t)/I(t) lim t tends to +infinite E(t)= lim t tends to +infinite E(t)/I(t)=
Interpret your answers.
A. In the long term, U.S. exports to the country will fall without bound and be 0.3 times U.S. imports from the country.
B. In the long term, U.S. exports to the country will rise without bound and be 0.3 times U.S. imports from the country.
C. In the long term, U.S. imports from the country will rise without bound and be 0.3 times U.S. exports to the country.
D. In the long term, U.S. imports from the country will fall without bound and be 0.3 times U.S. exports to the country.
Comment on the results.
A. In the real world, imports and exports can rise without bound. Thus, the given models can be extrapolated far into the future.
B. In the real world, imports and exports can fall without bound. Thus, the given models can be extrapolated far into the future.
C. In the real world, imports and exports do not change, they always stay fixed. Thus, the given models should not be extrapolated far into the future.
D. In the real world, imports and exports cannot rise without bound. Thus, the given models should not be extrapolated far into the future.

Answer 1

Follows are the responses to this question:

Explanation:

For point 1:

Clearly
`\lim_(t \to +\infty) E(t) = + \infty \ and \ \lim_(t \to +\infty) (E(t))/(I(t)) = 0.3`

For point 2:

The second option is the answer to this question because exports are going to increase 0.3 times unbound.

For point 3:

It's the last choice because it would be in the real world, and it cannot rise without bounds.