QUESTION 3
iii
Easy
The initial population of a village is 750. Every year, 50 people move from a nearby city to the village.
Find an expression that relates P and t, and explain why it represents linear growth.
SOLUTION
A linear growth is represented by the general formula
\(P = P_{0} + (r × t)\)
From the given data, we have
\(P_{0} = 750\)
\(r = 50\)
Substituting these into the formula, we get
\(P = 750 + 50t\)
This represents a linear growth because the population increases by a fixed amount every year.
\(P = P_{0} + (r × t)\)
From the given data, we have
\(P_{0} = 750\)
\(r = 50\)
Substituting these into the formula, we get
\(P = 750 + 50t\)
This represents a linear growth because the population increases by a fixed amount every year.
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Final Answer : \(P = 750 + 50t\)
Concept Note
Linear growth happens when a quantity increases by a fixed amount per unit of time. Its general form is
\(P = P_{0} + (r × t)\),
where
\(P = \) population after \(t\) years
\(P_{0} = \) initial population
\(r = \) annual increase
\(t = \) number of years