Calculus; Limits
posted by James on .
The percentage of research articles in a prominent journal written by researchers in the United States can be modeled by
A(t) = 26 + (36/1 + 0.8(0.8)^−t'),
where t is time in years (t = 0 represents 1983). Numerically estimate
lim as t→+infinity A(t).
I calculated
A(t)= 26 + (36/1 + 0.8(0.8)^−1983)
and got nothing.(0.8(0.8)^−1983)< this doesn't work)
Also
Interpret the answer. (Does it have anything to do with the answer? The percentage I mean, if there is, how do i determine the answer below?)
A.In the long term, the percentage of research articles in the journal written by researchers in the U.S. approaches 26%.
B.In the long term, the percentage of research articles in the journal written by researchers in the U.S. approaches 36%.
C.In the long term, the number of research articles in the journal written by researchers in the U.S. approaches 26
D.In the long term, the percentage of research articles in the journal written by researchers in the U.S. approaches 0%.
Don't know why its wrong. Help Please. Thank you.

if your a(t) is correct, then your limit should be 62. from what i see, you have 26+36+.64^t. if that is the case, then you should combine like terms and then you should have 62+.64^t. Well that .64^t will be 1/.64^t and when you apply the infinity and its under 1 that resultant will always be 0 leaving you with the answer being 62