According to Kleiber's Law, the metabolic rate P (in kilocalories per day) and body mass m (in kilograms) of an animal are related by a three-quarter power law given below. Estimate the increase in metabolic rate when body mass increases from 65 to 66 kg. (Round your answer to one decimal place.)

P = 73.3m3/4

Well, according to Kleiber's Law, the metabolic rate is related to body mass by a three-quarter power law. That means we can estimate the increase in metabolic rate when body mass increases from 65 kg to 66 kg using the formula P = 73.3m^(3/4).

So, let's calculate the metabolic rate for a body mass of 65 kg first:
P1 = 73.3(65^(3/4))

And then calculate the metabolic rate for a body mass of 66 kg:
P2 = 73.3(66^(3/4))

To find the increase in metabolic rate, we subtract the initial metabolic rate from the final metabolic rate:
Increase in metabolic rate = P2 - P1

Now, let's do some math and get the answer. But be careful, math can be metabolic-ly demanding!

Calculating...calculating...calculating...

Drum roll, please...

The increase in metabolic rate when body mass increases from 65 kg to 66 kg is approximately X kilocalories per day. (Sorry, my clown calculations took a wrong turn and got lost in the circus of numbers.)

To estimate the increase in metabolic rate when body mass increases from 65 to 66 kg, you can plug in the values into the given formula and calculate the difference.

First, calculate the metabolic rate (P) for a body mass of 65 kg:
P1 = 73.3 * (65^3/4)

Next, calculate the metabolic rate (P) for a body mass of 66 kg:
P2 = 73.3 * (66^3/4)

Finally, calculate the difference in metabolic rate:
Increase = P2 - P1

Let's plug in the values and calculate the increase:

P1 = 73.3 * (65^3/4)
P1 ≈ 73.3 * (1570.091)
P1 ≈ 115,054.46 (approximately)

P2 = 73.3 * (66^3/4)
P2 ≈ 73.3 * (1662.026)
P2 ≈ 121,964.89 (approximately)

Increase = P2 - P1
Increase ≈ 121,964.89 - 115,054.46
Increase ≈ 6,910.43 (approximately)

Therefore, the estimated increase in metabolic rate when body mass increases from 65 to 66 kg is approximately 6,910.4 kilocalories per day.

To estimate the increase in metabolic rate when body mass increases from 65 to 66 kg using Kleiber's Law, we need to calculate the value of P for both masses and then find the difference.

Let's calculate P for a body mass of 65 kg:
P₁ = 73.3(65)^(3/4)

Now, let's calculate P for a body mass of 66 kg:
P₂ = 73.3(66)^(3/4)

To find the increase in metabolic rate, we subtract P₁ from P₂:
Increase in metabolic rate = P₂ - P₁

Now let's do the calculations:

P₁ = 73.3(65)^(3/4)
P₁ ≈ 73.3(15728.81)^(3/4)
P₁ ≈ 73.3(13.212)
P₁ ≈ 967.99 kcal/day (rounded to two decimal places)

P₂ = 73.3(66)^(3/4)
P₂ ≈ 73.3(17145.50)^(3/4)
P₂ ≈ 73.3(13.279)
P₂ ≈ 973.61 kcal/day (rounded to two decimal places)

Increase in metabolic rate = P₂ - P₁
Increase in metabolic rate ≈ 973.61 - 967.99
Increase in metabolic rate ≈ 5.62 kcal/day (rounded to two decimal places)

Therefore, the estimated increase in metabolic rate when body mass increases from 65 to 66 kg is approximately 5.6 kcal/day.

(66/65)^(3/4) = 1.0115

The metabolic rate increases by 1.15%
Call it 1.2% after rounding.