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Amrita who is a microbiologist observes in the laboratory that a new bacterium on the slide expands its population at the rate of 12% every hour. If the current population of the bacteria is 4,000,000 units, then what is the population of the bacteria on the slide after 3 hours?

Amrita who is a microbiologist observes in the laboratory that a new bacterium on the slide expands its population at the rate of 12% every hour. If the current population of the bacteria is 4,000,000 units, then what is the population of the bacteria on the slide after 3 hours? Correct Answer 5,619,712 units

Given:

The population expansion rate of the Bacterium = 12%

Current population of the Bacteria = 4,000,000 units

Concept:

If a population of bacteria increases/decreases at the rate of ‘R%’ per unit time, then the population of bacteria after time ‘n’ will be,

Pnew = Poriginal ­× {(100 ± R)/100}n

where,

Poriginal = Original quantity

Pnew = Quantity after increase decrease

R = Rate of Increase/Decrease of quantity

n = Time

Calculation:

The population of the bacteria after three hours,

Pnew = Poriginal ­× {(100 ± R)/100}n

⇒ Pnew = 4,000,000 × {(100 + 12)/100}3

⇒ Pnew = 4,000,000 × (112/100) × (112/100) × (112/100)

⇒ Pnew = 4,000,000 × 1,404,928/1,000,000

⇒ Pnew = 4 × 1,404,928

⇒ Pnew = 5,619,712 units

∴ The population of the bacteria after three hours 5,619,712 units.

Shortcut Trick

The population of the bacteria after three hours,

Pnew = Poriginal ­× {(100 ± R)/100}n

⇒ Pnew = 4,000,000 × {(100 + 12)/100}3

⇒ Pnew = 4,000,000 × (112/100) × (112/100) × (112/100)

⇒ Pnew = 4 × 112 × 112 × 112

We don't need to do the complete calculation. We will use the unit digit multiplication method.

Unit digit product = 4 × 2 × 2 × 2

⇒ 32 

Since the unit digit is 2. 

So, We will choose the option which has its unit digit as 2 i.e. option 4) 5,619,712 units.

∴ The population of the bacteria after three hours 5,619,712 units. 

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