Question

the figure to the right gives the number of farms in millions from 1920 (t = 20) to 2000 (t = 100). in what year was the number of farms decreasing most rapidly? in, the number of farms was decreasing most rapidly.

Explanation:

Step1: Recall the concept of rate of change

The rate of change of a function (in this case, the number of farms over time) is related to the slope of the tangent line to the graph of the function. A negative slope indicates a decreasing function, and the more negative the slope, the more rapidly the function is decreasing.

Step2: Analyze the graph

Looking at the graph of the number of farms versus time, we need to find the point where the slope of the tangent line is most negative. By visual inspection of the given graph, we can see that the steepest - descending part (where the function is decreasing most rapidly) occurs around \(t = 50\) (since \(t\) represents the number of years after 1900).

Step3: Calculate the year

Since \(t\) is the number of years after 1900 and \(t = 50\), the year is \(1900 + 50=1950\)

Answer:

1950