Question

the table shows the proportional relationship between a hedgehogs weight loss and the number of days of 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\tchange in weight (oz)
12\t-0.36
24\t-0.72
75\t-2.25
102\t-3.06

the hedgehogs total change in weight over 115 days is
(type an integer or a decimal.)

Explanation:

Step1: Calculate the weight - loss rate

To check if the relationship is proportional, find the ratio of weight loss to days for each pair. For the first pair: $\frac{- 0.36}{12}=-0.03$. For the second pair: $\frac{-0.72}{24}=- 0.03$. For the third pair: $\frac{-2.25}{75}=-0.03$. For the fourth pair: $\frac{-3.06}{102}=-0.03$. Since the ratio is constant ($k = - 0.03$), the relationship is proportional.

Step2: Calculate the weight loss in 115 days

Use the formula $y = kx$, where $x = 115$ and $k=-0.03$. So, $y=-0.03\times115=-3.45$.

Answer:

-3.45