QUESTION 3
i
Easy
The initial population of a village is 750. Every year, 50 people move from a nearby city to the village.
Find the population of the village after 6 years.
SOLUTION
1
Identify initial population and yearly increase
Initial population \(P_0 = 750\)
Increase per year \(= 50\) people
Increase per year \(= 50\) people
2
Calculate population after 6 years
\(\begin{aligned} P &= 750 + 50 × 6 \\ &= 750 + 300 \\ &= 1050\end{aligned}\)
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Final Answer : Population after \(6\) years \(= 1050\)
Concept Note
When a quantity(like population) increases by a fixed number every year, the total after a given number of years is the initial amount plus the yearly increase multiplied by the number of years, i.e.,
\(P_{n} = P_{0} + (n × r)\),
where
\(P_{n} = \) population after \(n\) years
\(P_{0} = \) initial population
\(r = \) annual increase(fixed number)
\(n = \) number of years