Question

the price he charges for an order of cumin (in dollars) as a function of the size of the order (in kilograms) is graphed. what is the approximate average rate at which the total cost increases, as the order size increases from 100 to 600 kilograms? choose 1 answer: 1.50 dollars per kilogram 1.80 dollars per kilogram 2.10 dollars per kilogram 2.40 dollars per kilogram

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 \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\). Here, \(x\) represents the size of the order (in kilograms) and \(y\) represents the price (in dollars). Let \(x_1 = 100\), \(x_2=600\). From the graph, when \(x = 100\), \(y=f(100)=300\) (approximate value by looking at the graph's \(y\) - coordinate when \(x = 100\)), and when \(x = 600\), \(y=f(600)=1200\) (approximate value by looking at the graph's \(y\) - coordinate when \(x = 600\)).

Step2: Substitute the values into the formula

Substitute \(x_1 = 100\), \(x_2 = 600\), \(f(x_1)=300\), and \(f(x_2)=1200\) into the formula \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\). We get \(\frac{1200 - 300}{600-100}=\frac{900}{500}=1.8\)

Answer:

B. 1.80 dollars per kilogram