Many of our absorption equations are of the form where and k are positive parameters, and

Question:

Many of our absorption equations are of the form

where α and k are positive parameters, and where r(0) = 0, lim_{c → ∞}r(c) = ∞ and r'(c) > 0. In each of the following cases, identify r(c) and show that α(c) is increasing. Use L'Hopital's rule to find the limit as c → ∞, and use the method of leading behavior to describe absorption near c = 0 and c = ∞.

1. α(c) = Ac / k + c (from Table 3.1).

2. α(c) = Ac² / k + c² (from Table 3.1).

3. α(c) = Acⁿ / k + cⁿ for some positive value of n.

4. Try without plugging in a particular form for r(c).