Polynomials | Class 9 Mathematics Notes

2.4 LINEAR GROWTH AND LINEAR DECAY

This section formalizes the concepts of linear growth and linear decay using real-world examples modeled by linear functions. Linear growth is characterized by a quantity increasing by a fixed amount over equal intervals, while linear decay involves a quantity decreasing similarly. An example of linear growth is the cost of a journey given by C(d) = 100 + 60d, where the cost increases by ₹60 for every additional kilometer traveled. A table illustrates the cost for distances from 0 to 5 km. Linear decay is exemplified by the height of water in a tank decreasing over months, modeled by h(t) = 3 - 0.5t, with a table showing water height decreasing by 0.5 m each month. The section includes exercises for students to calculate values using these linear functions, make tables of values, and interpret the expressions as models of growth or decay. This section strengthens understanding of linear functions as tools to represent changing quantities in practical contexts.

📊 Diagram: Table on page 9 (2×6); Table on page 10 (2×6)

🧪 Activity: Exercises involve calculating values from linear functions, making tables, and interpreting growth and decay.

🔗 Connection: Prepares for understanding linear relationships between variables in the next section.

Table on page 9 (2×7)

Table on page 10 (2×6)