A mobile phone is bought for ₹10,000. Its value decreases by ₹800 every year.
Find the value of the phone after 3 years.
(i) The initial value of the mobile phone is ₹10,000. Every year, its value decreases by a constant amount of ₹800.
To find the value after 3 years, we calculate the total depreciation over 3 years:
Subtracting this from the initial value, the value of the phone after 3 years is:
∴ The value of the phone after 3 years is ₹7,600.
Make a table of values for varying from 0 to 8 years and show how the value of the phone, , depreciates with time.
(ii) The table of values showing how the value v depreciates with time t (from 0 to 8 years) is as follows:
| Time ( years) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|---|
| Value ( in ₹) | 10000 | 9200 | 8400 | 7600 | 6800 | 6000 | 5200 | 4400 | 3600 |
Find an expression that relates and , and explain why it represents linear decay.
(iii) The expression that relates the value v and time t is:
This represents linear decay because as the value of t increases by a fixed number (one year), the value of v decreases by a fixed number (₹800). Since the quantity decreases by a constant amount over equal intervals, it forms a linear pattern.
Explanation
The question tests the concept of linear decay, where a quantity decreases by a constant amount over equal intervals. The initial value acts as the constant term, and the yearly decrease acts as the coefficient of the variable , forming the linear equation:
The table clearly demonstrates this constant difference of 800 between consecutive values.