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While studying her family’s history. Shikha discovers records of ancestors 12 generations back. She wonders how many ancestors she has had in the past 12 generations. She starts to make a diagram to help her figure this out. The diagram soon becomes very complex.
While studying her family’s history. Shikha discovers records of ancestors 12 generations back. She wonders how many ancestors she has had in the past 12 generations. She starts to make a diagram to help her figure this out. The diagram soon becomes very complex. (a) Make a table and a graph showing the number of ancestors in each of the 12 generations, (b) Write an equation for the number of ancestors in a given generation n
(a) Make a table and a graph showing the number of ancestors in each of the 12 generations.
(b) Write an equation for the number of ancestors in a given generation n.

Solution:

Given, Shikha discovers records of ancestors 12 generations back.

She wonders how many ancestors she has had in the past 12 generations.

(a) We have to make a table and a graph showing the number of ancestors in each of the 12 generations.

It is clear every past generation has twice as many people as this generation.

Past Generation Number Number of ancestors
1 1
2 2 × 1 = 2 = 21
3 2 × 2 = 4 = 22
4 4 × 2 = 8 = 23
5 8 × 2 = 16 = 24
6 16 × 2 = 32 = 25
7 32 × 2 = 64 = 26
8 64 × 2 = 128 = 27
9 128 × 2 = 256 = 28
10 256 × 2 = 512 = 29
11 512 × 2 = 1024 = 210
12 1024 × 2 = 2048 = 211

While studying her family’s history. Shikha discovers records of ancestors 12 generations back. She wonders how many ancestors she has had in the past 12 generations. She starts to make a diagram to help her figure this out. The diagram soon becomes very complex. (a) Make a table and a graph showing the number of ancestors in each of the 12 generations, (b) Write an equation for the number of ancestors in a given generation n

(b) We have to write an equation for the number of ancestors in a given generation n.

Form the above table,

We observe that the number of ancestors will be 2ⁿ.

✦ Try This: Express 4.375 × 10⁶ in usual form.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12

NCERT Exemplar Class 8 Maths Chapter 8 Problem 137

While studying her family’s history. Shikha discovers records of ancestors 12 generations back. She wonders how many ancestors she has had in the past 12 generations. She starts to make a diagram to help her figure this out. The diagram soon becomes very complex. (a) Make a table and a graph showing the number of ancestors in each of the 12 generations, (b) Write an equation for the number of ancestors in a given generation n

Summary:

(a) A table and a graph showing the number of ancestors in each of the 12 generations is mentioned above, (b) An equation for the number of ancestors in a given generation n is 2ⁿ.

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