The circulation time of a mammal (that is, the average time it takes for all the blood in the body to circulate once and return to the heart) is proportional to the fourth root of the body mass of the mammal. (a) Write a formula for the circulation time, T, in terms of the body mass B. Use k as the constant of proportionality. T = k (B) (b) If an elephant of body mass 5230 kilograms has a circulation time of 148 seconds, find the constant of proportionality, k. Round your answer to one decimal place. k = Number (c) What is the circulation time of a human with body mass 60 kilograms? Round your answer to the nearest integer. The human circulation time is about Number seconds.

Question

Haiden Davis

Biology

5 March, 02:04

The circulation time of a mammal (that is, the average time it takes for all the blood in the body to circulate once and return to the heart) is proportional to the fourth root of the body mass of the mammal. (a) Write a formula for the circulation time, T, in terms of the body mass B. Use k as the constant of proportionality. T = k (B) (b) If an elephant of body mass 5230 kilograms has a circulation time of 148 seconds, find the constant of proportionality, k. Round your answer to one decimal place. k = Number (c) What is the circulation time of a human with body mass 60 kilograms? Round your answer to the nearest integer. The human circulation time is about Number seconds.

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Answers (1)

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Hadley Irwin · Answer 1

(a) T = k (B) ^1/4

(b) k is 17.4

(c) The human circulation time is about 49 seconds

Explanation:

(a) The circulation time T is directly proportional to the fourth root of the body mass B

Mathematically, T = k (B) ^1/4

(b) When T = 148 s, B = 5230 kg

K = T / (B) ^1/4 = 148 / (5230) ^1/4 = 148/8.5 = 17.4

(c) T = k (B) ^1/4

k = 17.4, B = 60 kg

T = 17.4 (60) ^1/4 = 17.4*2.8 = 48.72 = 49 s (to the nearest integer)