Ex 2.4, 1

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Ex 2.4, 1 Suppose a plant has height 1.75 feet and it grows by 0.5 feet each month. (i) Find the height after 7 months. (ii) Make a table of values for t varying from 0 to 10 months and show how the height, h, increases every month. (iii) Find an expression that relates h and t, and explain why it represents linear growth. Given that a plant has height 1.75 feet and it grows by 0.5 feet each month. Thus, Initial Height = 1.75 feet Height after 1 month = 1.75 + 0.5 = 2.25 feet Height after 2 months = 1.75 + 0.5 × 2 = 1.75 + 0.5 = 2.5 feet Similarly, we can write Height after 7 months = 1.75 + 0.5 × 7 = 1.75 + 3.5 = 175/100+35/10 = 175/100+350/100 = (175 + 350)/100 = 525/100 = 5.25 feet Now, our (ii) question is (ii) Make a table of values for t varying from 0 to 10 months and show how the height, h, increases every month. Finding height after each month Initial Height = Height after 0 months = 1.75 feet Height after 1 month = 1.75 + 0.5 = 2.25 feet Height after 2 months = 1.75 + 0.5 × 2 = 1.75 + 1 = 2.75 feet Height after 3 months = 1.75 + 0.5 × 3 = 1.75 + 1.5 = 3.25 feet Height after 4 months = 1.75 + 0.5 × 4 = 1.75 + 2 = 3.75 feet Height after 5 months = 1.75 + 0.5 × 5 = 1.75 + 2.5 = 4.25 feet Height after 6 months = 1.75 + 0.5 × 6 = 1.75 + 3 = 4.75 feet Height after 7 months = 1.75 + 0.5 × 7 = 1.75 + 3.5 = 5.25 feet Height after 8 months = 1.75 + 0.5 × 8 = 1.75 + 4 = 5.75 feet Height after 9 months = 1.75 + 0.5 × 9 = 1.75 + 4.5 = 6.25 feet Height after 10 months = 1.75 + 0.5 × 10 = 1.75 + 5 = 6.75 feet Thus, Height increases by 0.5 feet every month Writing it in a table Let Time in months = t And, height of plant (in feet) after t months be h(t) Writing it in a table Now, our (iii) question is (iii) Find an expression that relates h and t, and explain why it represents linear growth. Let Time in months = t And, height of plant (in feet) after t months be h(t) Since height h starts at 1.75 and adds 0.5 every month t Our Expression is h(t) = 1.75 + 0.5t Explanation of Linear Growth It represents linear growth because the height increases by a constant amount (0.5 feet) over equal intervals of time (each month).