The dynamics of an age-structured population are modeled in a later section. For certain parameter values the long-term per capita growth rate of the population is given by r = 1/2(1 + \sqrt{1+8s} ),
where s is the annual survival probability of juveniles.
(a) Approximate the growth rate with a Taylor polynomial of degree one (linear approximation) centered at 0. (b) Approximate the growth rate with a Taylor polynomial of degree two centered at 0.