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In a forest in Alberta, every year 70% of the population of red deer either die of natural causes or are eaten by predators. There are 9 new red deer per square kilometer. Given the discrete-time dynamical system x_t+1 = 0.3 * x_t + 9, and the initial condition x_0 = 15, find a formula for the solution of the system in terms of t.

Solve a discrete-time dynamical system modeling the red deer population in Alberta, where 70% of the population decreases annually and 9 new deer are added each year. With the given recurrence relation x_t+1 = 0.3 * x_t + 9, we derive the solution based on the initial condition x_0 = 15. Ideal for high school students learning about recurrence relations and population models.

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