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Life Science : Bacteria can divide in every 20 minutes. So 1 bacterium can multiply to 2 in 20 minutes. 4 in 40 minutes, and so on. How many bacteria will there be in 6 hours? Write your answer using exponents, and then evaluate

Solution:

Given, Bacteria can divide in every 20 minutes

1 bacterium can multiply to 2 in 20 minutes, 4 in 40 minutes, and so on.

We have to find the number of bacteria that will be there in 6 hours.

We know, 1 hour = 60 minutes

So, 6 hours = 6 × 60

= 360 minutes

Bacteria multiples in every 20 minutes

Number of times bacteria will multiply in 6 hours = 360/20

= 36/2

= 18

For any non-zero integers ‘a’ and whole numbers m

a × a × a⋯ m times = a^m

Here, a = 2 and m = 18

a^m = 2¹⁸

Therefore, Bacteria that will be there in 6 hours = 2¹⁸

2¹⁸ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

= 8 × 8 × 8 × 8 × 8 × 8

= 64 × 64 × 64 × 64

= 262144

Therefore, number of bacteria = 262144

✦ Try This: The cell of a bacteria doubles in every 30 min. A scientist begins with a single cell. How many cells will be there after 24 hours

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 13

NCERT Exemplar Class 7 Maths Chapter 11 Problem 93

Life Science : Bacteria can divide in every 20 minutes. So 1 bacterium can multiply to 2 in 20 minutes. 4 in 40 minutes, and so on. How many bacteria will there be in 6 hours? Write your answer using exponents, and then evaluate

Summary:

Bacteria can divide in every 20 minutes. So 1 bacterium can multiply to 2 in 20 minutes. 4 in 40 minutes, and so on. The number of bacteria that will be there in 6 hours is 2¹⁸. On evaluating we get 262144.

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