Ex 2.4, 4

Transcript

Ex 2.4, 4 A telecom company charges ₹600 for a certain recharge scheme. This prepaid balance is reduced by ₹15 each day after the recharge. Write an equation that models the remaining balance b(x) after using the scheme for x days. Explain why it represents linear decay. After how many days will the balance run out? (iii) Make a table of values for x varying from 1 to 10 days and show how the balance b(x), reduces with time. Given that telecom company charges ₹600. And, this prepaid balance is reduced by ₹15 each day after the recharge. Thus, Initial Balance = ₹ 600 Balance after 1 day = 600 – 15 = ₹ 585 Balance after 2 days = 600 – 15 × 2 = 600 – 30 = ₹ 570 Balance after 3 days = 600 – 15 × 3 = 600 – 45 = ₹ 555 Let Number of days = x And, balance (in ₹) after x days be b(x) We can write b(x) = 600 – 15x Explanation of Linear Decay It represents linear decay because the balance decreases by a constant amount (₹15) every equal interval (every day). Now, our (ii) question is (ii) After how many days will the balance run out? Our expression is b(x) = 600 – 15x We need to find value of x when b(x) = 0 Putting b(x) = 0 in our equation 0 = 600 – 15x 0 + 15x = 600 15x = 600 x = 600/15 x = 40 Thus, after 40 days the balance runs out Now, our (iii) question is (iii) Make a table of values for x varying from 1 to 10 days and show how the balance b(x), reduces with time. Our expression is b(x) = 600 – 15x Finding value after each day (starting from 1) Balance after 1 day = 600 – 15 = ₹ 585 Balance after 2 days = 600 – 15 × 2 = 600 – 30 = ₹ 570 Balance after 3 days = 600 – 15 × 3 = 600 – 45 = ₹ 555 Balance after 4 days = 600 – 15 × 4 = 600 – 60 = ₹ 540 Balance after 5 days = 600 – 15 × 5 = 600 – 75 = ₹ 525 Balance after 6 days = 600 – 15 × 6 = 600 – 90 = ₹ 510 Balance after 7 days = 600 – 15 × 7 = 600 – 105 = ₹ 495 Balance after 8 days = 600 – 15 × 8 = 600 – 120 = ₹ 480 Balance after 9 days = 600 – 15 × 9 = 600 – 135 = ₹ 465 Balance after 10 days = 600 – 15 × 10 = 600 – 150 = ₹ 450 Thus, balance decreases by ₹ 50 every month Writing it in a table Time (Days) Balance (₹) 1 585 2 570 3 555 4 540 5 525 6 510 7 495 8 480 9 465 10 450