MathematicsIn 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 1st year = 40,000……………….(ii)
    The rate of incrementation in trees = 5%
    Therefore, the increased number of trees at the end of 1st year=40,000+5% of 40,000
    =40,000+(5100×40,000)
    =40,000+2000
    =42,000
    The number of trees at the end of 1st year =42,000 And, for the numbers of  trees at the start of 2nd year = 42,000
    The increased number of trees at the end of 2nd  year=42,000+5% of 42,000
    =42,000+(5100×42,000)
    =42,000+2100
    =44100
    The number of trees at the end of 2nd year =44,100 And, for the numbers of  trees at the start of 3rd year = 44,100
    The increased number of trees at the end of 3rd  year=44,100+5% of 44,100
    =44,100+(5100×44,100)
    =44,100+2205
    =46,305
    The number of trees at the end of 3rd 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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