Question

noah and a sibling are going to make their favorite dinner. to find the ingredients, they use a rideshare service from their home to wnc farmers market. this graph represents function d, which gives his distance from the farmers market, in miles, m minutes since leaving his home.

1. estimate the average rate of change over noahs entire route. interpret this quantity for the context of the situation. type a response

Explanation:

Step1: Identify two - point for rate calculation

We need two points \((t_1,d_1)\) and \((t_2,d_2)\) on the graph. Let's take the starting point \((0,18)\) (when \(t = 0\) minutes, \(d=18\) miles) and the ending point \((18,0)\) (when \(t = 18\) minutes, \(d = 0\) miles).

Step2: Calculate the rate of change

The rate of change (average speed) formula is \(r=\frac{\Delta d}{\Delta t}=\frac{d_2 - d_1}{t_2 - t_1}\). Substitute \(d_1 = 18\), \(t_1=0\), \(d_2 = 0\), \(t_2 = 18\) into the formula: \(r=\frac{0 - 18}{18-0}=\frac{- 18}{18}=-1\) mile per minute.

Answer:

The average rate of change is - 1 mile per minute. This means that, on average, the distance from the farmers market is decreasing by 1 mile per minute as time passes during the entire route.