# problem-12.9

problem-12.9 We can fit both using the same starting values and compare:

    > l =  function(t,a,b,k,t0) (a + b*t)*(1 - exp(-k*(t-t0)))
    > l1 = function(t,a,k,t0) l(t,a,0,k,t0)
    > res.l = nls(length ~ l(age,a,b,k,t0), data=reddrum,
    +  start=c(a=32,b=.25,k=.5,t0=0))
    > res.l1 = nls(length ~ l1(age,a,k,t0), data=reddrum,
    + start=c(a=32,k=.5,t0=0))
    > AIC(res.l)
    [1] 306.7
    > AIC(res.l1)
    [1] 376.2

So the more complicated model is better by this criteria.
(The point of the paper that this data came from is to show that both of these models pale in comparison to the more complicated one they presented, which takes into account seasonal growth and a decrease in growth rate due to age.)