Question

this graph shows the total distance in city blocks, $d(t)$, that pilar walked as a function of time in minutes, $t$.
determine the average rate of change between $t = 20$ and $t = 90$.
$\frac{1}{10}=0.1$
edit my response
what do you think the average rate of change you calculated means in this situation?

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) over the interval \([x_1,x_2]\) is \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\). In this case, \(x=t\), \(y = d(t)\), \(x_1=20\), and \(x_2 = 90\).

Step2: Assume values from the graph (since the graph is not fully shown, but we know the rate calculation result).

Let's assume \(d(20)=a\) and \(d(90)=b\). The average rate of change \(\frac{d(90)-d(20)}{90 - 20}=\frac{b - a}{70}\). If the result is \(\frac{1}{10}=0.1\), it means that for every 1 - minute increase in time \(t\) (from \(t = 20\) to \(t=90\)), the distance \(d(t)\) (in city - blocks) increases by \(0.1\) city - blocks.

Answer:

The average rate of change of \(0.1\) means that Pilar walked at an average speed of \(0.1\) city - blocks per minute between \(t = 20\) minutes and \(t=90\) minutes.