Question
A biologist uses the formula E=km^(2)/(4) to model the relationship between the mass of a bird's egg, E grams, and the mass of the bird, m grams. The number k is a constant that is close to 0.25 for healthy eggs. a) A ruby-throated hummingbird has a mass of 3.4 g. What is the mass of its egg? b) An ostrich egg has a mass of 1.4 kg. What is the mass of the mother bird? c) A 7.3 -kg whooping crane lays an egg whose mass is 208 g Does this bird appear to be healthy? Explain.
Solution
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Zayden
Expert · Tutor for 3 years
Answer
**a) Mass of hummingbird egg:*** Given: m = 3.4 g, k ≈ 0.25* Formula: E = km^(2/4) = km^(1/2)* Calculation: E = 0.25 * (3.4)^(1/2) * E ≈ 0.25 * 1.84* E ≈ 0.46 gTherefore, the mass of the hummingbird's egg is approximately 0.46 grams.**b) Mass of the mother ostrich:*** Given: E = 1.4 kg = 1400 g (since 1 kg = 1000 g), k ≈ 0.25* Formula: E = km^(1/2)* Rearranging the formula to solve for m: m = (E/k)^2* Calculation: m = (1400/0.25)^2* m = (5600)^2* m = 31,360,000 g* m = 31,360 kg (since 1000 g = 1 kg)Therefore, the mass of the mother ostrich is approximately 31,360 kg.**c) Health of the whooping crane:*** Given: m = 7.3 kg = 7300 g, E = 208 g, k ≈ 0.25* We will calculate the expected egg mass for a healthy whooping crane with a mass of 7.3 kg using the given formula and compare it to the actual egg mass.* Calculation: E = 0.25 * (7300)^(1/2)* E ≈ 0.25 * 85.44* E ≈ 21.36 gThe expected mass of a healthy whooping crane's egg is approximately 21.36 g. The actual egg mass is 208 g, which is significantly larger (almost 10 times larger) than the expected mass.Therefore, based on this model, the whooping crane does *not* appear to be healthy. The egg is much larger than expected for a bird of that mass. There could be various reasons for this discrepancy, including measurement error, individual variation, or a health issue affecting the bird or the egg.