A telecom company charges ₹ 600 for a certain recharge scheme. This prepaid balance is reduced Class 9

A telecom company charges ₹ 600 for a certain recharge scheme. This prepaid balance is reduced Class 9

Question 1.

A telecom company charges ₹ 600 for a certain recharge scheme. This prepaid balance is reduced by ₹ 15 each day after the recharge. Class 9

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.

Solution:

i. Initial balance = ₹600

Daily reduction of balance = ₹15

Let x represent the number of days and b(x) represent the remaining balance

Remaining balance

= Initial balance - (Daily reduction of balance × Number of days)

∴ b(x) = 600 - 15 x

The above equation represents linear decay because each day, the balance is reduced by the same amount of ₹15.

ii. The balance runs out when,

b(x) = 0

∴ 600 - 15 x = 0

∴ 15 x = 600

∴ x = $\frac{600}{15}$ = 40

∴ The balance will run out after 40 days.

iii.