The population of certain community follows the law of exponential change. If the present population of the community is 144,000 and ten years ago was 110,000 when will the population double? In ten years, what will be the population of the community
Answers
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Given :-
- The present population of the community is 144,000.
- Ten years ago was 110,000.
To Find :-
- In ten years, what will be the population of the community ?
Solution :-
we know that, exponential change for population say that,
- Amount after growth = Original Amount(1 + r%)^Time
Given that,
→ Population before 10 years = 110000 = Original Amount.
→ Present Population = Amount after growth.
→ Time = 10years.
→ Rate = let r % .
So,
Putting all values we get,
→ 144000 = 110000(1 + r%)¹⁰
→ (144000/110000) = (1 + r%)¹⁰
→ (144/110) = (1 + r%)¹⁰ --------- Equation (1).
Now, we have to find population after 10 years.
So,
→ Original Amount = 144000
→ Time = 10 years.
→ Amount after growth = New Population
Putting values we get,
→ New Population = 144000 * (1 + r%)¹⁰
Putting value of Equation (1) now,
→ New Population = 144000 * (144/110)
→ New Population ≈ 188509 . (Ans.)
Hence, Population after 10 years will be 188509.
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