Calculating Population Growth Time
This problem involves calculating the time it takes for a population to grow to a specific amount given a constant annual growth rate. We can use the formula for compound growth, similar to compound interest.
Given Information
- Present Population (P): 1,000
- Future Population (A): 1,331
- Annual Growth Rate (r): 10% or 0.10
- Number of Years (n): To be determined
Population Growth Formula
The formula for population growth is:
$A = P (1 + r)^n$
Step-by-Step Calculation
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Substitute the known values into the formula:
$1,331 = 1,000 (1 + 0.10)^n$
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Simplify the expression inside the parenthesis:
$1,331 = 1,000 (1.1)^n$
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Isolate the term with the exponent by dividing both sides by 1,000:
$\frac{1,331}{1,000} = (1.1)^n$
$1.331 = (1.1)^n$
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Determine the value of n. We need to find what power of 1.1 equals 1.331. We can test values or recognize the pattern:
- $(1.1)^1 = 1.1$
- $(1.1)^2 = 1.21$
- $(1.1)^3 = 1.331$
Therefore, n = 3.
Conclusion
It will take 3 years for the town's population to reach 1,331.
Similar Questions
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Important Questions from Compound Interest
At what rate percent per annum will Rs. 7200 amount to Rs. 7938 in one year, if interest is compounded half yearly?
What is the compound interest (in Rs.) on a sum of Rs. 8192 for \(1 \frac{1}{4}\) years at 15% per annum, if interest is compounded 5-monthly ?
What is the difference (in Rs.) between the interests on Rs. 50,000 for one year at 8% per annum compounded half yearly and yearly?
A sum of money becomes Rs. 11,880 after 4 years and Rs. 17,820 after 6 years on compound interest, if the interest is compounded annually. What is the half of the sum (in Rs.)?
A sum invested at compound interest amounts to Rs. 7,800 in 3 years and Rs. 11,232 in 5 years. What is the rate per cent?
