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.

# 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.

1. A
42,000
2. B
44,100
3. C
46,305
4. D
None of these

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### 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 ${1}^{\mathit{st}}$ year = 40,000……………….(ii)
The rate of incrementation in trees = 5%
Therefore, the increased number of trees at the end of
$=40,000+\left(\frac{5}{100}×40,000\right)$
$=40,000+2000$
$=42,000$
The number of trees at the end of ${1}^{\mathit{st}}$ year $=42,000$ And, for the numbers of  trees at the start of ${2}^{\mathit{nd}}$ year = 42,000
The increased number of trees at the end of
$=42,000+\left(\frac{5}{100}×42,000\right)$
$=42,000+2100$
$=44100$
The number of trees at the end of ${2}^{\mathit{nd}}$ year $=44,100$ And, for the numbers of  trees at the start of ${3}^{\mathit{rd}}$ year = 44,100
The increased number of trees at the end of
$=44,100+\left(\frac{5}{100}×44,100\right)$
$=44,100+2205$
$=46,305$
The number of trees at the end of ${3}^{\mathit{rd}}$ 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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