The following table describes a seven-stage model for the life cycle of the loggerhead turtle.

The corresponding Leslie matrix is given by

Suppose that the number of turtles in each stage of the initial turtle population is described by the vector
x0 = (200,000 130,000 100,000 70,000 500 400 1100)T
(a) Enter L in MATLAB and then set
x0 = (200000, 130000, 100000, 70000, 500, 400, 1100)€²
Use the command
x50 = round(L^50*x0)
to compute x50. Compute also the values of x100, x150, x200, x250, and x300.
(b) Loggerhead turtles lay their eggs on land. Suppose that conservationists take special measures to protect these eggs and as a result the survival rate for eggs and hatchlings increases to 77 percent. To incorporate this change into our model, we need only change the (2, 1) entry of L to 0.77. Make this modification to the matrix L and repeat part (a). Has the survival potential of the loggerhead turtle improved significantly?
(c) Suppose that instead of improving the survival rate for eggs and hatchlings we could devise a means of protecting the small juveniles so that their survival rate increases to 88 percent. Use equations (7) and (8) from Application 3 of Section 3 to determine the proportion of small juveniles that survive and remain in the same stage and the proportion that survive and grow to the next stage. Modify your original matrix L accordingly and repeat part (a) using the new matrix. Has the survival potential of the loggerhead turtle improved significantly?

Table 1 Seven-Stage Model for Loggerhead Turtle Demographies Stage Number Description (age in years) Annual Survivorship 0.6747 0.7857 0.6758 0.7425 08091 0.8091 0.8091 Eggs Laid per Year 0 0 Eggs, hatchlings (