Question

The weight y of a fiddler crab is directly proportional to the 1.25 power of the weight x of its claws. A crab with a body weight of x grams has claws weighing y grams. Estimate the weight of a fiddler crab with claws weighing x grams.

OPTION 1: 1.25 grams
OPTION 2: 1.50 grams
OPTION 3: 1.75 grams
OPTION 4: 2.00 grams

Answer 1

The weight of a fiddler crab with claws weighing x grams can be estimated as (y/k)^0.8 grams. Option 4: 2.00 grams is the closest estimate.

Step-by-step explanation:

The relationship between the weight y of a fiddler crab and the weight x of its claws can be expressed as:

y = kx^1.25

Where k is the constant of proportionality. To estimate the weight of a fiddler crab with claws weighing x grams, we can rearrange the equation:

y = kx^1.25

x = (y/k)^(1/1.25)

x = (y/k)^0.8

So, the weight of the fiddler crab with claws weighing x grams would be (y/k)^0.8 grams. Therefore, Option 4: 2.00 grams is the closest estimate.