hye - jin is a chef who caters korean food for parties and other events. she buys a cargo van to transport…

hye - jin is a chef who caters korean food for parties and other events. she buys a cargo van to transport ingredients and supplies for her business. the graph shows the projected value of her van as it ages.\nwhat is the best estimate for the average rate of change of her vans value, in thousands of dollars, when it ages from 2 years to 5 years?\nvan\nvalue (thousands of dollars)\n40\n36\n32\n28\n24\n20\n16\n12\n8\n4\n0\n1 2 3 4 5 6\nage (yr)

hye - jin is a chef who caters korean food for parties and other events. she buys a cargo van to transport ingredients and supplies for her business. the graph shows the projected value of her van as it ages.\nwhat is the best estimate for the average rate of change of her vans value, in thousands of dollars, when it ages from 2 years to 5 years?\nvan\nvalue (thousands of dollars)\n40\n36\n32\n28\n24\n20\n16\n12\n8\n4\n0\n1 2 3 4 5 6\nage (yr)

Answer

Explanation:

Step1: Identify the formula for average rate of change

The formula for the average rate of change of a function $y = f(x)$ from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 2$, $b = 5$, and $y$ represents the value of the van in thousands of dollars.

Step2: Determine the values of $f(2)$ and $f(5)$ from the graph

From the graph, when $x = 2$, the value of the van $y=f(2)=26$ (in thousands of dollars), and when $x = 5$, the value of the van $y = f(5)=7$ (in thousands of dollars).

Step3: Calculate the average rate of change

Substitute the values into the formula: $\frac{f(5)-f(2)}{5 - 2}=\frac{7 - 26}{3}=\frac{- 19}{3}\approx - \frac{13}{1}=-13$.

Answer:

$-13$