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 125 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) 12 -0.24 26 -0.52 68 -1.36 97 -1.94 the hedgehog’s total change in weight over 125 days is (type an integer or a decimal.) ounces.

Explanation:

Step1: Find the constant of proportionality

First, we determine the rate of weight loss per day (constant of proportionality \(k\)) using the formula \(k=\frac{\text{Change in Weight}}{\text{Days of Hibernation}}\). For the first row: \(k = \frac{- 0.24}{12}=- 0.02\). Let's check with the second row: \(\frac{-0.52}{26}=-0.02\), third row: \(\frac{-1.36}{68}=-0.02\), fourth row: \(\frac{-1.94}{97}=-0.02\). So the constant of proportionality is \(-0.02\) oz per day.

Step2: Calculate weight loss for 125 days

Now, to find the weight loss over 125 days, we use the formula \(\text{Change in Weight}=k\times\text{Days of Hibernation}\). Substituting \(k = - 0.02\) and days \( = 125\), we get \(\text{Change in Weight}=-0.02\times125=-2.5\).

Answer:

\(-2.5\)