The variation in a population is modelled by the recurrence relation

(Jn+1 0.9257 0.0208) (Jn) + (0.014)

(An+1 0.0661 0.9767) (An) (0.056)

where Jn and An are the sizes, in millions, of the subpopulations of
juveniles and adults, respectively, n years after 1 January 2010. On that
date there were 4.17 million juveniles and 17.24 million adults. Choose the
option that gives the total population, in millions, to two decimal places,
predicted by the model for 1 January 2011.
Options
A 21.33 B 21.40 C 21.68 D 21.83
E 22.14 F 22.21 G 22.25 H 22.36

Thanks.

To calculate the total population one year later, on 1 January 2011, using the given model and initial population sizes, we need to find the values of Jn+1 and An+1.

According to the recurrence relation:

(Jn+1 0.9257 0.0208) (Jn) + (0.014)
(An+1 0.0661 0.9767) (An) (0.056)

We can substitute the initial values for Jn and An, which are 4.17 million and 17.24 million, respectively.

(J1 0.9257 0.0208) (4.17) + (0.014)
(A1 0.0661 0.9767) (17.24) (0.056)

To calculate J1, we multiply the given matrix (J1 0.9257 0.0208) by the initial juvenile population size (4.17 million). Then add the constant term (0.014).

J1 = (4.17 * 0.9257) + (4.17 * 0.0208) + 0.014

To calculate A1, we multiply the given matrix (A1 0.0661 0.9767) by the initial adult population size (17.24 million). Then add the constant term (0.056).

A1 = (17.24 * 0.0661) + (17.24 * 0.9767) + 0.056

Next, we need to calculate the total population for 1 January 2011 by adding the values of J1 and A1.

Total population = J1 + A1

After performing these calculations, the option that gives the total population to two decimal places will be the answer.