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

To find the total population predicted by the model for 1 January 2011, we need to calculate the sum of the sizes of the juvenile and adult subpopulations.

We are given the initial sizes of the subpopulations on 1 January 2010:
Juvenile population (J0) = 4.17 million
Adult population (A0) = 17.24 million

Using the given recurrence relation, we can calculate the sizes of the subpopulations for 1 January 2011.

For the juvenile population (Jn+1):
Jn+1 = 0.9257 * Jn + 0.0208 * An + 0.014

Substituting the values:
J1 = 0.9257 * 4.17 + 0.0208 * 17.24 + 0.014

Similarly, for the adult population (An+1):
An+1 = 0.0661 * Jn + 0.9767 * An + 0.056

Substituting the values:
A1 = 0.0661 * 4.17 + 0.9767 * 17.24 + 0.056

To find the total population, we add the sizes of the juvenile and adult populations:
Total Population = J1 + A1

Simplifying the equations and calculating the values will give us the answer.