Question

The following graph shows data regarding the population of a town in thousands. At what rate was the population​ changing?

Answer 1

Notice those two points on the "linear graph", the first point is at (1965 , 140) and the second point is at (1990 , 100).

the rate or average rate of change, namely the slope will then be 

$\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~{{ 1965}} &,&{{140}}~) % (c,d) &&(~{{ 1990}} &,&{{ 100}}~) \end{array} \\\\\\ % slope = m slope = {{ m}}\implies \cfrac{\stackrel{rise}{{{ y_2}}-{{ y_1}}}}{\stackrel{run}{{{ x_2}}-{{ x_1}}}}\implies \cfrac{100-140}{1990-1965}\implies \cfrac{-40}{25}\implies -\cfrac{8}{5}$

Answer 2

Answer: -1.6

Step-by-step explanation:

For a graph of a function, the rate of change of function is the slope of the line.

The slope of a line passing from (a,b) and (c,d) is given by :-

$m=\dfrac{d-b}{c-a}$

In the given picture, we are given a graph having two points (1965,140) and (1990,100).

Now, the rate of change of the function is given by :-

$m=\dfrac{100-140}{1990-1965}=\dfrac{-40}{25}=-1.6$

Hence, the population was ​ changing at the rate of -1.6 people per year.