Male bees hatch from unfertilized eggs and females from fertilized ones. Therefore, femalebees have two biological parents but males have only one. Conjecture and prove a formulafor the number Fn+1 and Mp+1 of female and male ancestors, respectively, in the (n + 1)stprevious generation of a male bee as a function of the numbers F, and M, in the nth previousgeneration, n > 1. (Notice that F1 = 1 and M1 = 0.) Your formulas are examples of functions%3Dcalled recurrence relations.Remark: You have 2 biological parents, 22 biological grandparents, 23 biological great-grandparents, etc.you. This pattern cannot continue indefinitely, however. If it did, then your 40th previousgeneration would contain 240 ancestors, which far exceeds the total number of people whohave ever lived. The pigeonhole principle implies that everyone’s ancestral tree must stopbranching eventually. A similar analysis applies to bees, of course. The requested formulaassumes that the branching continues indefinitely, but the result should be approximatelyIn principle, there are 2" ancestors in the nth generation precedingvalid for an actual bee for modest values of n.

For a male drone there is only one female parent while for a female worker there are two parents(one…

Male bees hatch from unfertilized eggs and females from fertilized ones. Therefore, female bees have two biological parents but males have only one. Conjecture and prove a formula for the number Fn+1 and Mµ+1 of female and male ancestors, respectively, in the (n + 1)st previous generation of a male bee as a function of the numbers F, and M, in the nth previous generation, n > 1. (Notice that F1 = 1 and M1 = 0.) Your formulas are examples of functions %3D called recurrence relations.

Male bees hatch from unfertilized eggs and females from fertilized ones. Therefore, female bees have two biological parents but males have only one. Conjecture and prove a formula for the number Fn+1 and Mµ+1 of female and male ancestors, respectively, in the (n + 1)st previous generation of a male bee as a function of the numbers F, and M, in the nth previous generation, n > 1. (Notice that F1 = 1 and M1 = 0.) Your formulas are examples of functions %3D called recurrence relations.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Male bees hatch from unfertilized eggs and females from fertilized ones. Therefore, female
bees have two biological parents but males have only one. Conjecture and prove a formula
for the number Fn+1 and Mp+1 of female and male ancestors, respectively, in the (n + 1)st
previous generation of a male bee as a function of the numbers F, and M, in the nth previous
generation, n > 1. (Notice that F1 = 1 and M1 = 0.) Your formulas are examples of functions
%3D
called recurrence relations.
Remark: You have 2 biological parents, 22 biological grandparents, 23 biological great-
grandparents, etc.
you. This pattern cannot continue indefinitely, however. If it did, then your 40th previous
generation would contain 240 ancestors, which far exceeds the total number of people who
have ever lived. The pigeonhole principle implies that everyone’s ancestral tree must stop
branching eventually. A similar analysis applies to bees, of course. The requested formula
assumes that the branching continues indefinitely, but the result should be approximately
In principle, there are 2" ancestors in the nth generation preceding
valid for an actual bee for modest values of n.

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