Ex 2.4, 3

Transcript

Ex 2.4, 3 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. (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. Given that initial population of a village is 750. Every year, 50 people move from a nearby city to the village. Thus, Initial Population = 750 Population after 1 year = 750 + 50 = 800 Population after 2 years = 750 + 50 × 2 = 750 + 100 = 850 Population after 3 years = 750 + 50 × 3 = 750 + 150 = 900 Similarly, we can write Population after 6 years = 750 + 50 × 6 = 750 + 300 = 1,050 Now, our (ii) question is (ii) Make a table of values for t varying from 0 to 10 years and show how the population, P, increases every year. Finding value after each year Initial Value = Value after 0 years = ₹ 10,000 Initial Population = Population after 0 years = 750 Population after 1 year = 750 + 50 = 800 Population after 2 years = 750 + 50 × 2 = 750 + 100 = 850 Population after 3 years = 750 + 50 × 3 = 750 + 150 = 900 Population after 4 years = 750 + 50 × 4 = 750 + 200 = 950 Population after 5 years = 750 + 50 × 5 = 750 + 250 = 1,000 Population after 6 years = 750 + 50 × 6 = 750 + 300 = 1,050 Population after 7 years = 750 + 50 × 7 = 750 + 350 = 1,100 Population after 8 years = 750 + 50 × 8 = 750 + 400 = 1,150 Population after 9 years = 750 + 50 × 9 = 750 + 450 = 1,200 Population after 10 years = 750 + 50 × 10 = 750 + 500 = 1,250 Thus, population increases by 50 every month Writing it in a table Now, our (iii) question is (iii) Find an expression that relates P and t, and explain why it represents linear growth. Let Time in years = t And, Population of the village after t years be P(t) Since population is initially 750 and increases by 50 every year Our Expression is P(t) = 750 + 50t Explanation of Linear Growth It represents linear growth because the population increases by a constant amount (50 people) every year.