Mathematics
The initial population of a village is 750. Every year, 50 people move from a nearby city to the village.
(i) Find the population of the village after 6 years.
(ii) Make a table of values for t varying from 0 to 10 years and show how the population, P, increases every year.
(iii) Find an expression that relates P and t, and explain why it represents linear growth.
Answer
Initial population of the village = 750
Increase in population per year = 50
(i) Population of the village after 6 years = 750 + 50 × 6
= 750 + 300
= 1050
∴ The population of the village after 6 years is 1050.
(ii) The population of the village at the end of t years is given by P = 750 + 50t.
| Year, t | Population, P |
|---|---|
| 0 | 750 |
| 1 | 800 |
| 2 | 850 |
| 3 | 900 |
| 4 | 950 |
| 5 | 1000 |
| 6 | 1050 |
| 7 | 1100 |
| 8 | 1150 |
| 9 | 1200 |
| 10 | 1250 |
(iii) The expression relating P and t is:
P = 750 + 50t
This represents linear growth because as t (years) increases by 1, the population P increases by a constant amount of 50 people. The change in P for every unit change in t is the same, which is the characteristic feature of linear growth.
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