Question

1. function f models the population, in thousands, of a city t years after 1930. the average rate of change of f from t = 0 to t = 70 is approximately 14 thousand people per year. is this value a good way to describe the population change of the city over that time period? explain or show your reasoning.

Explanation:

The average rate of change only describes the overall total change divided by the time span, masking the non-linear trend of the population. The graph shows the population grew slowly at first, then accelerated rapidly after ~1970 (t=40). The average rate of 14 thousand/year does not reflect this shift in growth speed, so it fails to capture the actual pattern of population change over the period.

Answer:

No, this value is not a good way to describe the population change. The average rate of change only represents the overall total population increase divided by the 70-year span, but the graph shows the population growth was not constant: it grew slowly in the early decades and much more quickly in later decades. The average rate does not account for this non-linear, accelerating growth pattern, so it does not accurately reflect how the population changed over the full time period.