The cells of a bacteria double in every 30 minutes. A scientist begins with a single cell. How many cells will be there after (a) 12 hours (b) 24 hours

Solution:

Given, the cells of a bacteria double in every 30 minutes.

A scientist begins with a new cell.

(a) We have to find the number of cells after 12 hours.

Cells in bacteria in the beginning = 1

Cells in bacteria after 30 minutes = 2

After 1 hour, cells in bacteria = 2² = 4

Cells of bacteria after 12 hours = (2²)¹²

Using law of exponents,

(a^m)ⁿ = a^mn

= 2^{2 × 12}

= 2²⁴

Therefore, 2²⁴ cells will be there after 12 hours.

(b) We have to find the number of cells after 24 hours.

Cells of bacteria after 24 hours = (2²)²⁴

Using law of exponents,

(a^m)ⁿ = a^mn

= 2^{2 × 24}

= 2⁴⁸

Therefore, 2⁴⁸ cells will be there after 24 hours.

✦ Try This: The cells of a bacteria double in every 30 minutes. A scientist begins with a single cell. How many cells will be there after 36 hours.

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

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NCERT Exemplar Class 8 Maths Chapter 8 Problem 124

The cells of a bacteria double in every 30 minutes. A scientist begins with a single cell. How many cells will be there after (a) 12 hours (b) 24 hours

Summary:

The cells of a bacteria double in every 30 minutes. A scientist begins with a single cell. 2²⁴ and 2⁴⁸ cells will be there after (a) 12 hours (b) 24 hours.

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