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A male bee comes from an unfertilised egg, i.e - Leaving Cert Mathematics - Question b - 2016
Question b
A male bee comes from an unfertilised egg, i.e. he has a female parent but does not have a male parent. A female bee comes from a fertilised egg, i.e. she has a fema... show full transcript
Worked Solution & Example Answer:A male bee comes from an unfertilised egg, i.e - Leaving Cert Mathematics - Question b - 2016
Step 1
Continue the diagram to G5
Answer
From the given pattern in the diagram, we can observe the following:
- G5 has 5 ancestors: Female, Male, Female, Female, Male. Thus, the complete diagram continues to G5 as:
G1 G2 G3 G4 G5
Female → Female → Male → Male → Female Male → Female → Male → Female → Male Male → Female → Male → Male → Female
Step 2
Step 3
Use this formula to verify the number of ancestors in G3
Answer
To verify the number of ancestors in G3 using the formula:
[ G_3 = \frac{(1 + \sqrt{5})^3 - (1 - \sqrt{5})^3}{2^3 \sqrt{5}} ]
Calculating:
[ G_3 = \frac{(1+\sqrt{5})^3 - (1-\sqrt{5})^3}{8\sqrt{5}} ] [ = \frac{(1 + 3\sqrt{5} + 3 \cdot 5 + \sqrt{125}) - (1 - 3\sqrt{5} + 3 \cdot 5 - \sqrt{125})}{8\sqrt{5}} ] [ = \frac{16 + 8\sqrt{5}}{8\sqrt{5}} ] [ = 2 ]
This matches our previous calculation revealing that G3 has 2 ancestors.