Question

Suppose there are $60$ bees in a beehive. The number of bees doubles every hour. How many bees will be there after $100$ hours?

• A. $60\times 100$
• B. $60\times 2^{100-1}$
• C. $60\times 2\times 100$
• D. $60\times 2^{100}$

Answer 1

The correct option is D $60\times 2^{100}$

Initially, there are $60$ bees in a beehive. Every hour the number of bees gets doubled.

Hence,

$\bullet$ After $\underset{–}{1\text{hour}}$, the number of bees $=60\times 2=\underset{–}{60\times 2^1}$

$\bullet$ After $\underset{–}{2\text{hours}}$, the number of bees $=60\times 2^1\times 2^1=60\times 2^{1+1}=\underset{–}{60\times 2^2}$

$\bullet$ After $\underset{–}{3\text{hours}}$, the number of bees $=60\times 2^1\times 2^1\times 2^1=60\times 2^{1+1+1}=\underset{–}{60\times 2^3}$
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$\bullet$ Similarly, after $\underset{–}{100\text{hours}}$, the number of bees $=\underset{–}{60\times 2^{100}}$

Hence, option (d.) is the correct choice.