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In a forest, there are 40,000 trees. Find the expected number of trees after 3 years if the objective is to increase the number at the rate of 5% per year.

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42,000

44,100

46,305

None of these

answer is C.

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Detailed Solution

Concept- Finding the expected number of trees after 3 years
Total number of trees in the forest = 40,000………………(i)
The number of trees at the start of

1^{st}

year = 40,000……………….(ii)
The rate of incrementation in trees = 5%
Therefore, the increased number of trees at the end of

1^{st} year = 40, 000 + 5 % of 40, 000

= 40, 000 + (\frac{5}{100} \times 40, 000)

= 40, 000 + 2000

= 42, 000

The number of trees at the end of

1^{st}

year

= 42, 000

And, for the numbers of trees at the start of

2^{nd}

year = 42,000
The increased number of trees at the end of

2^{nd} year = 42, 000 + 5 % of 42, 000

= 42, 000 + (\frac{5}{100} \times 42, 000)

= 42, 000 + 2100

= 44100

The number of trees at the end of

2^{nd}

year

= 44, 100

And, for the numbers of trees at the start of

3^{rd}

year = 44,100
The increased number of trees at the end of

3^{rd} year = 44, 100 + 5 % of 44, 100

= 44, 100 + (\frac{5}{100} \times 44, 100)

= 44, 100 + 2205

= 46, 305

The number of trees at the end of

3^{rd}

year

= 46, 305

So, the number of trees after 3 years is 46,305.
Hence, the correct answer is option 3.

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In a forest, there are 40,000 trees. Find the expected number of trees after 3 years if the objective is to increase the number at the rate of 5% per year.

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