The remaining balance after x days is b(x) = 600 minus 15x. The balance becomes zero after 40 days. This represents linear decay because the balance decreases by the same 15 rupees every day.
A telecom company charges rupees 600 for a certain recharge scheme. This prepaid balance is reduced by rupees 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.
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(i) (The prepaid balance is represented by:
b(x) = 600 – 15x
Here, x shows the number of days and b(x) shows the remaining balance. This is a linear decay because the balance decreases regularly by 15 rupees every day. The reduction is constant, so the graph forms a straight line with a negative slope.
(ii) To find when the balance becomes zero:
600 – 15x = 0
Adding 15x:
15x = 600
Dividing by 15:
x = 40
Therefore, the prepaid balance will completely run out after 40 days.
(iii) To show how the prepaid balance reduces over time, we calculate the values of b(x) = 600 – 15x for x ranging from 1 to 10 days.
On Day 1, the balance is 600 – 15(1) = 585 rupees.
On Day 2, it is 600 – 15(2) = 570 rupees.
On Day 3, it is 600 – 15(3) = 555 rupees.
On Day 4, it is 600 – 15(4) = 540 rupees.
On Day 5, it is 600 – 15(5) = 525 rupees.
On Day 6, it is 600 – 15(6) = 510 rupees.
On Day 7, it is 600 – 15(7) = 495 rupees.
On Day 8, it is 600 – 15(8) = 480 rupees.
On Day 9, it is 600 – 15(9) = 465 rupees.
On Day 10, it is 600 – 15(10) = 450 rupees.
This structured breakdown clearly illustrates the steady, uniform daily loss of 15 rupees.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2 Introduction to Linear Polynomials (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-2/