QUESTION 2
iii
Easy
A mobile phone is bought for ₹10000. Its value decreases by ₹800 every year. Find an expression the relates v and t, and explain why it represents linear decay.
SOLUTION
A linear decay is represented by the general formula
\(v = v_{0} + (r × t)\)
From the given data, we have
\(v_{0} = 750\)
\(r = 800\)
Substituting these into the formula, we get
\(v = 10000 − 800t\)
This expression represents linear decay because \(v\) decreases by a fixed amount (\(800\)) for each unit increase in \(t\).
\(v = v_{0} + (r × t)\)
From the given data, we have
\(v_{0} = 750\)
\(r = 800\)
Substituting these into the formula, we get
\(v = 10000 − 800t\)
This expression represents linear decay because \(v\) decreases by a fixed amount (\(800\)) for each unit increase in \(t\).
🏆
Final Answer : \(v = 10000 − 800t\)
Concept Note
Linear decay happens when a quantity decreases by a fixed amount per unit of time. Its general form is
\(v = v_{0} + (r × t)\),
where
\(v = \) value after \(t\) years
\(v_{0} = \) initial value
\(r = \) annual decrease
\(t = \) number of years