Distinguish between linear growth (increasing at constant rate) and linear decay (decreasing at constant rate).
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Define linear growth and decay.
Linear growth happens when a quantity increases by a fixed amount over equal intervals.
For example, if a journey costs a fixed base fare plus ₹60 for every additional kilometer, the total cost experiences linear growth. The relationship can be modeled by a straight line with a positive slope.
Worked example from Example 10.
Problem. The height of water in a cylindrical tank is m at the start of summer. The height m at the end of months is given by the linear function:
Faded example based on Exercise 2.4 Q1.
Suppose a plant has an initial height of feet and it grows by a constant amount each month. We want to find the height after months if the growth rate is feet per month, and then write the linear growth function.
First, identify the initial value (y-intercept) and the rate of change (slope). The plant grows at a constant rate, meaning we add feet for every month that passes.
To find the specific height after months, multiply the rate by the number of months and add the initial height: feet.
We can generalize this pattern as a linear relationship since the quantity increases by a fixed amount over equal intervals. The mathematical function relating height and time in months is .
Check understanding of growth vs decay equations.
A tank holds 500 liters of water. A leak causes it to lose 15 liters every day. After how many days will the volume of water be 200 liters?
Guided problem based on Exercise 2.4 Q2.
List the initial value, the rate of change, and the time.
State the general equation for linear decay.
Substitute the given values into your formula.
Show the arithmetic to find the final value.
State both the value after 3 years and the general expression.
Does your answer make sense logically?