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
2 Likes
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 |
Answered By
3 Likes
Related Questions
A mobile phone is bought for ₹10,000. Its value decreases by ₹800 every year.
(i) Find the value of the phone after 3 years.
(ii) Make a table of values for t varying from 0 to 8 years and show how the value of the phone, v, depreciates with time.
(iii) Find an expression that relates v and t, and explain why it represents linear decay.The initial population of a village is 750. Every year, 50 people move from a nearby city to the village.
(i) 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.A telecom company charges a fixed monthly fee and an additional cost per GB of the internet data used. A student observes that when she used 10 GB, her bill was ₹350. When she used 20 GB, her bill was ₹550. If the monthly bill y depends on the amount of data used, x (in GB), according to the relation y = ax + b, Can you guess what the numbers 20 and 150 in the equation y = 20x + 150 represent?
A learning platform charges a fixed monthly fee and an additional cost per digital learning module accessed. A student observes that when she accessed 10 modules, her bill was ₹400. When she accessed 14 modules, her bill was ₹500. If the monthly bill y depends on the number of modules accessed, x, according to the relation y = ax + b, find the values of a and b.