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3. In Lab, Section II, Exercise 3 if dad and mom (first generation) have two children (second generation), how many descendants will there be in the following six generations if each child has the same number of children as their parents (22)? Complete the table below, then construct a line graph. Sign, date and prepare an image of your graph and include it with this lab report.

User Jjei
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Final answer:

The exercise is a mathematical progression predicting descendants. Starting with two parents, if each generation has 22 children, the number of descendants grows dramatically each generation, resulting in over 3.5 million by the seventh generation.

Step-by-step explanation:

The question asks about predicting how many descendants will there be in the future generations, assuming each child has the same number of children as their parents (22 children per couple). This is a mathematical exercise involving geometric progression because with each generation, the number of individuals increases by a constant factor (in this case, 11 times since each child is half of a pair). Starting with the second generation, each pair of parents has 22 children, meaning in the third generation, there would be 11 pairs, each with 22 children, and so on.

Using the information given, here's how the table would look for the next six generations, with each generation doubling in number from the previous one:

  • First Generation: 2 parents
  • Second Generation: 22 children (11 times 2)
  • Third Generation: 242 grandchildren (11 times 22)
  • Fourth Generation: 2,662 great-grandchildren (11 times 242)
  • Fifth Generation: 29,282 great-great-grandchildren (11 times 2,662)
  • Sixth Generation: 322,102 great-great-great-grandchildren (11 times 29,282)
  • Seventh Generation: 3,543,122 great-great-great-great-grandchildren (11 times 322,102)

To visualize this growth, one could create a line graph, where the x-axis represents each generation, and the y-axis represents the number of descendants in that generation. A signature, date, and preparation of an image of the graph would complete the lab report obligation.

User Ahmad Boorghany
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