Question

The initial population of a village is 750. Every year, 50 people move from a nearby city to the village.

Accepted Answer

(i) Population after 6 years: The initial population of the village is 750. Every year, the population increases by 50 people. Therefore, the increase in population after 6 years will be: 50 × 6 = 300 Adding this to the initial population, the population after 6 years will be: 750 + 300 = 1050 ∴ The population after 6 years is 1050. (ii) Table of values: We calculate the population P for each year t from 0 to 10 by adding 50 to the previous year's population. The table is as follows: t (years) 0 1 2 3 4 5 6 7 8 9 10 --- --- --- --- --- --- --- --- --- --- --- --- P (population) 750 800 850 900 950 1000 1050 1100 1150 1200 1250 As shown in the table, the population increases every year by a constant value of 50. (iii) Expression relating P and t: The expression that relates P and t is: P = 750 + 50t (iv) Explanation of Linear Growth: This represents linear growth because it is in the form of a linear relationship: y = ax + b where a = 50 and b = 750. Additionally, the difference between consecutive terms in the sequence of population is a constant value (50), meaning the population increases by a fixed amount each year. — The problem involves calculating linear growth based on a constant rate of change. The initial value is 750 and the constant increase is 50 per year. For part (i), we multiply the rate by 6 years and add it to the initial value. For part (ii), we generate values by repeatedly adding 50. For part (iii), we formulate the linear equation P = 750 + 50t and…