Functions that increase at a decreasing rate are concave (their second derivatives are negative) and

Functions that increase at a decreasing rate are concave
(their second derivatives are negative) and functions that increase at an
increasing rate are convex (their second derivatives are positive). Compare the
power law, log-linear, and bounded intensity processes in which a,b > 0 as
to their convexity and concavity. How would this behavior affect the choice of
an intensity function?