Linear growth and linear decay

Linear expressions describe things that grow or shrink steadily.

Growth. A journey costs C(d) = 100 + 60d rupees for d km: 100, 160, 220, 280, … Each km adds the same ₹60. That is linear growth. 15 km costs 100 + 900 = ₹1000, and ₹700 pays for 10 km.

Decay. Water in a tank starts at 3 m and is h(t) = 3 – 0.5t after t months: 3, 2.5, 2, 1.5, 1. Each month takes off the same 0.5 m. That is linear decay. After 5 months: 0.5 m.

In short:

• linear growth: a quantity increases by the same amount over equal steps;
• linear decay: it decreases by the same amount over equal steps.

To build the expression: start with the first value, then add (growth) or subtract (decay) the fixed change times the number of steps.