Question

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: P = 73.3m^(3/4).

Estimate the increase in metabolic rate when body mass increases from 77 to 78 kg. (Round your answer to three decimal places.)

I tried to work this out twice by finding the derivative and plugging in 77 for m. I got 18.559 once and 18.529 the second time. So I'm guessing it's about 18-19, but I can't figure it out. Help?

Answer 1

What did you come up with for the derivative?

Answer 2

73.3(3/4)m^(-1/4)

Answer 3

And when I plug in 77, I get 18.559, which apparently isn't correct.

Answer 4

One sec...I think that derivative is not correct...

Answer 5

For clarity, that should be: \[219/(4x ^{1/4})\]

Answer 6

Um, yes please. Don't you just bring the exponent (3/4) down and multiply it by the coefficient (77.3) and then subtract one from the old exponent to get the new one (-1/4)?

Answer 7

Ok, so I caught a mistake I made also. Anyway, it should look like this:\[73.3m ^{3/4}\]\[(3/4)73.3m ^{3/4-4/4}\]

Answer 8

That should leave you with: \[219.9/(4x ^{1/4})\]

Answer 9

Isn't that what I had before? 73.3(3/4)m^(-1/4)? I get 18.559 for both at 77.

Answer 10

Yea, I see that it is. Anyway what I'm getting when I plug it in is:

@77 = 18.558
@78 = 18.449

A difference of .05977

Answer 11

Oh... so is the question asking for the difference?

Answer 12

Oh. I got it finally. I was 1/1000th off.