Question

The percentage of research articles in a prominent journal written by researchers in the United States can be modeled by
A(t) = 25 + (36/1 + 0.6(0.7)^−t'),
where t is time in years (t = 0 represents 1983). Numerically estimate
lim as t→+infinity A(t).

Answer 1

\[A(t) = 25 + \frac{ 36 }{ 1+0.6(0.7)^{-t} }\]

Answer 2

Estimate \[estimate \lim_{x \rightarrow +\infty}A(t) numerically. \]

Answer 3

perhaps numerically estimate literally means getting your scientific calculator out and putting some huge numbers in for \(t\), in which forget case about the rest of this

.....but note that:

\(\lim\limits_{t \to \infty} 0.6(0.7^{-t}) = 0.6 \lim\limits_{t \to \infty} \left( \dfrac{10}{7} \right)^{t} \)

And

\(\lim\limits_{t \to \infty} 25 + \dfrac{ 36 }{ 1+0.6(0.7)^{-t} } \)

\(= 25 + \dfrac{ 36 }{ 1+ \lim\limits_{t \to \infty} 0.6(0.7)^{-t} }\)