QUESTION 2
i
Easy
A mobile phone is bought for ₹10000. Its value decreases by ₹800 every year. Find the value of the phone after 3 years.
SOLUTION
1
Identify initial value and yearly decrease
Initial value \((v_0) =\) ₹ \(10000\)
Yearly decrease \((r) =\) ₹ \(800\)
Yearly decrease \((r) =\) ₹ \(800\)
2
Calculate value after \(3\) years
Using the linear decay formula, we get
\(\begin{aligned} v &= 10000 − 800 × 3 \\ &= 10000 − 2400 \\ &= \text{₹} 7600\end{aligned}\)
\(\begin{aligned} v &= 10000 − 800 × 3 \\ &= 10000 − 2400 \\ &= \text{₹} 7600\end{aligned}\)
🏆
Final Answer : Value of phone after \(3 \) years \(= \) ₹ \(7600\)
Concept Note
A linear pattern where a quantity decreases by a constant amount over equal intervals of time is called linear decay/depreciation, which is given by the general formula
\(v = v_0 − (r × t)\),
where
\(v = \) value after t years
\(v_0 = \) initial value
\(r = \) annual decrease(fixed amount)
\(t = \) number of years