Final Answer:
A) The rate of change from year 2 to year 7 can be calculated by finding the average rate of change, which is the difference in the function's values divided by the difference in the input values.
B) The greatest rate of change occurs during the interval C, from year 7 to year 9. (Option C)
Step-by-step explanation:
A) To find the rate of change from year 2 to year 7, we use the formula for average rate of change: Rate = Change in Output / Change in Input. In this context, the output is the function's values (perhaps representing some quantity like population or revenue), and the input is time in years. So, for the interval from year 2 to year 7, we calculate the difference in function values and divide it by the difference in years.
B) To determine the interval with the greatest rate of change, we should analyze the rate of change for each interval. The interval with the highest average rate of change will correspond to the greatest rate of change. In this case, it's from year 7 to year 9 (option C). This implies that during this interval, the function experiences the steepest increase or decrease.
Understanding and calculating rates of change help analyze the trends and dynamics of the function over time, providing valuable insights in various fields, from economics to biology.(Option C)