The initial population of a village is 750. Every year, 50 people move from a nearby city to the village. Class 9
The initial population of a village is 750. Every year, 50 people move from a nearby city to the village. Class 9
Question 1.
The initial population of a village is 750. Every year, 50 people move from a nearby city to the village. Class 9
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.
Solution:
Initial population of a village = 750
People moving to the village each year = 50
i. Number of years (t) = 6
Population of the village after t years = Initial population + (No. of people moving to village each year × t)
∴ Population of the village after 6 years
= 750 + (50 × 6)
= 750 + 300
= 1050
∴ The population of the village after 6 years will be 1050.
ii.
| Year (t) | Population (P) |
| 0 | 750 |
| 1 | 750 + 50 × 1 = 800 |
| 2 | 750 + 50 × 2 = 850 |
| 3 | 750 + 50 × 3 = 900 |
| 4 | 750 + 50 × 4 = 950 |
| 5 | 750 + 50 × 5 = 1000 |
| 6 | 750 + 50 × 6 = 1050 |
| 7 | 750 + 50 × 7=1100 |
| 8 | 750 + 50 × 8 = 1150 |
| 9 | 750 + 50 × 9 = 1200 |
| 10 | 750 + 50 × 10 = 1250 |
iii. The linear expression that relates the population of a village (P) and the number of years (f) is P = 750 + 50t
Every year the population of the village increases by a fixed amount of 50 people.
∴ It represents linear growth.