Mathematics
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.
Polynomials
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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 |
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