Final answer:
The initial value of the population is 19,820, and it is decreasing at a rate of 2% per year, which equates to an annual decrease of 396.4.
Step-by-step explanation:
The initial value of the population in the model f(x) = 19,820(0.98)^x is 19,820. This represents the population size at the start, which is when x equals zero. Since the base of the exponential function is 0.98, which is less than 1, the population is decreasing over time.
The growth or decay rate in this model is 2%, because each year the population is multiplied by 0.98, which indicates a reduction of 2% from the previous year. To calculate the population change for one year, we need to apply the rate to the initial population: 19,820 multiplied by 0.98, which gives us the population for the next year. Hence, the population decreases annually by 396.4 (2% of 19,820).