Answer:
The rate of change from year 1 to year 2 is - 2%.
The rate of change from year 9 to year 10 is -0.02%
The rate of change will be the same for all years.
Explanation:
While this seems an unlikely answer (why would the rate reamin the same every year?), it is the correct answer since we are told that one equation is valid for t years. With no other information, we must conclude the rate of change remains the same every year. The actual number by which the population shrinks is changing, but the rate remains the same.
The function P(t) = 227,000(.98)^t says that the initial population in year 0 is 227,000 [227,000(0.98)^0 = 227,000]. The factor (0.98) is the result of the expression (1-(0.02)^t). The 1 is the factor for the initial population and the -0.02 is the fraction of 1 by which the population declines each year (2%).
Initial population = 227,000 [227,000(0.98)^0 = 227,000
Year 1 population would be (227,000)*(1-0.02)^1 or (227,000)*(0.98)
Year 2 population would be (227,000)*(1-0.02)^2 or (227,000)*(0.98)^2
Year 9 population would be (227,000)*(1-0.02)^9 or (227,000)*(0.98)^9
Year 10 population would be (227,000)*(1-0.02)^10 or (227,000)*(0.98)^10
The change is the same every year (0.98).