Word Problem

[Obsession]

In history class one day, Gene started thinking about his ancestors. He wondered if he was related to any of the famous people from the Middle Ages. That night, he asked his father about it.


"Well," said Dad, "you were born in 1990. Let's assume that there is a new generation every 25 years. For each generation you go back, each ancestor leads to two more since each person also has a mother and father. Does that make sense?"

"I think so," said Gene. "So you and Mom are my two ancestors from the 1965 generation. If I go back one more generation to 1940 there were four ancestors from that generation, who are the parents of you and Mom, or my grandparents."

"You've got it," Dad replied. "Now try the following questions and see what you find."

1.If you go back to 1890, how many ancestors were there from that generation?

2.If you go back to 1790, how many ancestors were there from that generation?

3.Write a formula that will calculate the number of ancestors you have from any year in history.

4.Use your formula to calculate how many ancestors you have from the 1240 generation, during the Middle Ages.

---------------

I answered the first two questions using a factor tree (or whatever its called). The first one, 1890, Gene has 16 ancestors. Number 2, 1790, Gene has 256 ancestors.
I noticed that the number of ancestors in each generation doubles as we go back. Gene's parents from 1965 is double the number from the 1990 generation. Then 1940 has twice as many ancestors than 1965 and so on.

The only problem with this problem is...I don't know how to get the equation.

 

[Mrspi]

In history class one day, Gene started thinking about his ancestors. He wondered if he was related to any of the famous people from the Middle Ages. That night, he asked his father about it.


"Well," said Dad, "you were born in 1990. Let's assume that there is a new generation every 25 years. For each generation you go back, each ancestor leads to two more since each person also has a mother and father. Does that make sense?"

"I think so," said Gene. "So you and Mom are my two ancestors from the 1965 generation. If I go back one more generation to 1940 there were four ancestors from that generation, who are the parents of you and Mom, or my grandparents."

"You've got it," Dad replied. "Now try the following questions and see what you find."

1.If you go back to 1890, how many ancestors were there from that generation?

2.If you go back to 1790, how many ancestors were there from that generation?

3.Write a formula that will calculate the number of ancestors you have from any year in history.

4.Use your formula to calculate how many ancestors you have from the 1240 generation, during the Middle Ages.

---------------

I answered the first two questions using a factor tree (or whatever its called). The first one, 1890, Gene has 16 ancestors. Number 2, 1790, Gene has 256 ancestors.
I noticed that the number of ancestors in each generation doubles as we go back. Gene's parents from 1965 is double the number from the 1990 generation. Then 1940 has twice as many ancestors than 1965 and so on.

The only problem with this problem is...I don't know how to get the equation.

Wouldn't you need to find the number of generations between the year you were born and the year in question? You'd do that by subtracting the year in question from your birth year, to find out how many years have elapsed. Then, divide by 25 to find the number of generations (I'd use just the whole number part of your quotient!).

Let n = number of generations
n = INT[(birth year - target year) / 25]

note: INT means "integer part of the quotient" so disregard any remainder

You will have 2ⁿ ancestors when you go back n generations.

I hope this helps you.

 

[Obsession]

Okay, I get it.

So using the formula x = 2 ^ (1990 - Y)/25 would give me the answer -
1990 - 1240 = 750
750 / 25 = 30
2^30 = 1,073,741,824

right?