The formula B=0.4089M^(3)/(4) gives the bird inhalation rate, B cubic metres of air per day, for a bird with mass M kilograms. a) Rewrite the formula using radicals. b) Calculate the inhalation rate for each bird. i) a 4.5-kg bald eagle ii) a 8.0-kg Canada goose c) Determine the mass of a bird whose inhalation rate is twice that of the bald eagle. d) Is the mass in part c twice that of the bald eagle? Explain.

## Step 1: Rewrite the formula using radicals### The fractional exponent can be rewritten as a radical. is equivalent to or . Thus, the formula becomes or .## Step 2: Calculate the inhalation rate for a 4.5-kg bald eagle### Substitute into the formula: . The bald eagle's inhalation rate is approximately of air per day.## Step 3: Calculate the inhalation rate for an 8.0-kg Canada goose### Substitute into the formula: . The Canada goose's inhalation rate is approximately of air per day.## Step 4: Determine the mass of a bird whose inhalation rate is twice that of the bald eagle### The bald eagle's inhalation rate is approximately /day. Twice this rate is /day. We need to solve for in the equation . Dividing both sides by gives . Raising both sides to the power of gives . The mass of the bird is approximately kg.## Step 5: Determine if the mass in part c is twice that of the bald eagle and explain### The mass of the bald eagle is kg. Twice this mass is kg. The mass of the bird with twice the inhalation rate is kg, which is not twice the mass of the bald eagle. This is because the relationship between the mass and the inhalation rate is not linear, but rather follows a power law with an exponent of .