Population Calculation: Past Value
The question asks for the village population two years ago, given the current population and the annual growth rate. This requires reversing the compound growth formula.
Understanding Annual Growth
An annual increase of 8% means that each year, the population is multiplied by a factor of $1 + 0.08 = 1.08$. To find the population two years ago, we need to divide the current population by this factor twice.
Mathematical Approach
Let the population two years ago be $P$. The population after one year was $P \times (1.08)$. The population after two years (the current population) is $P \times (1.08) \times (1.08) = P \times (1.08)^2$. We are given the current population is 58,320.
Therefore, we need to solve the equation:
$ P \times (1.08)^2 = 58,320 $Calculating Past Population
- Calculate the growth factor squared: $(1.08)^2 = 1.1664$.
- Set up the equation to find $P$: $P \times 1.1664 = 58,320$.
- Solve for $P$ by dividing the current population by the squared growth factor: $ P = \frac{58,320}{1.1664} $
- Perform the division: $ P = 50,000 $
The population two years ago was 50,000.
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Important Questions from Percentage
A number p increased by p% of 99 equals 99 increased by 99% of p. What is (p + 51)% of 928 + 72?
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What is 12% of 4% of 7% of 2 × 10 6 ?
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If X is 12.25% more than Y. then Y is approximately_____ less than X.
