SME
Principles of Biology II
Animal form and function
Use this for “By Kleiber’s law a mammal’s basal rate is 70M0.75 kcal a day. What is it for a 64 kg person, and per kilogram?”
Chart
B(M) = 70M³ᐟ⁴
Log–log axes: a power law draws as a straight line.
This is an example. Type your own values to start a new problem.
B (kcal/day)
=
70
×
(
M (kg)
)
0.75
B/M
Rate per kilogram
calculated · kcal/(kg·day)
Formulas
B
=
70
×
M
0.75
1,584
=
70
×
64
0.75
B
M
=
B
M
24.75
=
1,584
64
Assumptions
•
Kleiber’s law fits mammals at rest: B = 70M3/4, with the body mass M in kg and the basal rate B in kcal a day.
•
Small animals burn more per kilogram: B ÷ M = 70M−1/4 falls as the mass grows.
•
On log–log axes the power law is a straight line with slope 3/4.
Step-by-step
WE KNOW
M = 64 kg
FIND
basal metabolic rate (B), rate per kilogram (B/M)
Step 1 · Find basal metabolic rate (B)
Use B = 70 × M0.75
Raise
the
mass
to
the
3
4
power,
times
70.
B
=
70
×
64
0.75
B
=
70
×
22.63
B
=
1,584
kcal/day
Step 2 · Find rate per kilogram (B/M)
Use B/M = B ÷ M
Share the rate among the kilograms.
B
M
=
1,584
64
B
M
=
24.75
kcal/(kg·day)
Check
Put the numbers back in. Both sides should match.
1,584
=
70
×
64
0.75
✓
24.75
=
1,584
64
✓
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