Question

hibernation. how much weight does the hedgehog lose during 115 days of hibernation? use pencil and paper. explain how you know that the relationship between the hedgehogs weight loss and the number of days of hibernation is proportional. weight loss of hedgehog days of hibernation change in weight (oz) 8 -0.16 24 -0.48 66 -1.32 91 -1.82 the hedgehogs total change in weight over 115 days is □ ounces (type an integer or a decimal.)

Explanation:

Step1: Find the rate of weight - loss per day

To check if the relationship is proportional, we find the rate of weight - loss per day for each data - point. The rate $r$ is given by $r=\frac{\text{Change in Weight}}{\text{Days of Hibernation}}$. For the first row: $r_1=\frac{- 0.16}{8}=-0.02$ ounces per day. For the second row: $r_2=\frac{-0.48}{24}=-0.02$ ounces per day. For the third row: $r_3=\frac{-1.32}{66}=-0.02$ ounces per day. For the fourth row: $r_4=\frac{-1.82}{91}=-0.02$ ounces per day. Since the rate of weight - loss per day is constant ($r = - 0.02$ ounces per day), the relationship between the hedgehog's weight loss and the number of days of hibernation is proportional.

Step2: Calculate the weight loss in 115 days

We use the formula $\text{Change in Weight}=r\times\text{Days of Hibernation}$. Substitute $r=-0.02$ ounces per day and $\text{Days of Hibernation}=115$ days. Then $\text{Change in Weight}=-0.02\times115=-2.3$ ounces.

Answer:

$-2.3$