Question

the table shows the proportional relationship between a hedgehog’s weight loss and the number of days of hibernation. how much weight does the hedgehog lose during 120 days of hibernation? use pencil and paper. explain how you know that the relationship between the hedgehog’s weight loss and the number of days of hibernation is proportional.
weight loss of hedgehog

days of hibernation	change in weight (oz)
20	-0.6
65	-1.95
101	-3.03

the hedgehog’s total change in weight over 120 days is \\(\square\\) ounces. (type an integer or a decimal )

Explanation:

Step1: Find the constant of proportionality

To determine the constant of proportionality \( k \), we use the formula for a proportional relationship \( y = kx \), where \( y \) is the change in weight (oz) and \( x \) is the number of days of hibernation. We can take the first pair of values: \( x = 7 \) days and \( y = -0.21 \) oz. So, \( k=\frac{y}{x}=\frac{-0.21}{7}=-0.03 \) oz per day. We can verify with another pair, e.g., \( x = 20 \), \( y = -0.6 \). Then \( k=\frac{-0.6}{20}=-0.03 \), which is the same. So the constant of proportionality is \( -0.03 \) oz per day.

Step2: Calculate weight loss for 120 days

Using the proportional relationship \( y = kx \), with \( k = -0.03 \) and \( x = 120 \) days. So \( y=-0.03\times120=-3.6 \) oz.

Answer:

\(-3.6\)