You have two parents, four grandparents, eight great-grandparents, and so forth. (a) If all your ancestors were distinct, what would be the total number of your ancestors for the past 41 generations (counting your parents' generation as number one)? (Hint: Use the formula for the sum of a geometric sequence.) (b) Assuming that each generation represents 25 years, how long (in years) is 41 generations? yr h (c) The total number of people who have ever lived is approximately 100 billion, which equals 1011 people. Compare this fact with the answer to part (a). What can you deduce? (Select all that apply.) People have been living on earth for less than 1,100 years. There could not have been 41 generations in my line of ancestry. Some ancestors on different branches of the family tree must be the same. Some of my ancestors must not have had children.
You have two parents, four grandparents, eight great-grandparents, and so forth. (a) If all your ancestors were distinct, what would be the total number of your ancestors for the past 41 generations (counting your parents' generation as number one)? (Hint: Use the formula for the sum of a geometric sequence.) (b) Assuming that each generation represents 25 years, how long (in years) is 41 generations? yr h (c) The total number of people who have ever lived is approximately 100 billion, which equals 1011 people. Compare this fact with the answer to part (a). What can you deduce? (Select all that apply.) People have been living on earth for less than 1,100 years. There could not have been 41 generations in my line of ancestry. Some ancestors on different branches of the family tree must be the same. Some of my ancestors must not have had children.
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter14: Sequences And Mathematical Induction
Section14.CR: Review Problem Set
Problem 37CR
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Transcribed Image Text:You have two parents, four grandparents, eight great-grandparents, and so forth.
(a) If all your ancestors were distinct, what would be the total number of your ancestors for the past 41 generations (counting your parents' generation as number one)?
(Hint: Use the formula for the sum of a geometric sequence.)
(b) Assuming that each generation represents 25 years, how long (in years) is 41 generations?
yr
(c) The total number of people who have ever lived is approximately 100 billion, which equals 1011 people. Compare this fact with the answer to part (a). What can you
deduce? (Select all that apply.)
People have been living on earth for less than 1,100 years.
There could not have been 41 generations in my line of ancestry.
Some ancestors on different branches of the family tree must be the same.
Some of my ancestors must not have had children.
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