A telecom company charges ₹600 for a certain recharge scheme. This prepaid balance is reduced by ₹15 each day after the recharge.
(i) Write an equation that models the remaining balance b(x) after using the scheme for x days. Explain why it represents linear decay.
(ii) 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.

Question

A telecom company charges ₹600 for a certain recharge scheme. This prepaid balance is reduced by ₹15 each day after the recharge.
(i) Write an equation that models the remaining balance b(x) after using the scheme for x days. Explain why it represents linear decay.
(ii) 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.

KnowledgeBoat · Accepted Answer

Initial balance = ₹600 Reduction per day = ₹15 (i) The remaining balance after x days is given by: b(x) = 600 - 15x This represents linear decay because as x (days) increases by 1, the balance b(x) decreases by a constant amount of ₹15. The change in b(x) for every unit change in x is a fixed decrease, which is the characteristic feature of linear decay. (ii) For the balance to run out, b(x) = 0. So, 600 - 15x = 0 ⇒ 15x = 600 ⇒ x = ⇒ x = 40 ∴ The balance will run out after 40 days. (iii) The balance after x days is given by b(x) = 600 - 15x. | Days, x | Balance, b(x) (₹) | | ------- | ----------------: | | 1 | 585 | | 2 | 570 | | 3 | 555 | | 4 | 540 | | 5 | 525 | | 6 | 510 | | 7 | 495 | | 8 | 480 | | 9 | 465 | | 10 | 450 |

Mathematics

Polynomials

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