Question

iris picked a bucket of raspberries to make jam. the table shows the cups of raspberries left in the bucket, y, as a function of the number of batches of jam she makes, x. is the rate of change positive or negative? negative find and describe the rate of change of the function. the rate of change is \boxed{} it represents ? in the amount of raspberries in the bucket for each batch iris makes. batches, x raspberries left in bucket (cups), y 1 16 4 10 7 4

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(\frac{y_2 - y_1}{x_2 - x_1}\).
Take two points from the table, e.g., \((1, 16)\) and \((4, 10)\).

Step2: Calculate rate of change

Substitute into the formula: \(\frac{10 - 16}{4 - 1}=\frac{-6}{3}=-2\).
Check with another pair, e.g., \((4, 10)\) and \((7, 4)\): \(\frac{4 - 10}{7 - 4}=\frac{-6}{3}=-2\).

Step3: Interpret the rate

A negative rate means the amount of raspberries is decreasing. The rate of \(-2\) means 2 cups less per batch.

Answer:

The rate of change is \(-2\). It represents a decrease in the amount of raspberries in the bucket for each batch Iris makes.