Q1.
What amount will be left on the 15th day? How many days will it take for the entire amount to be spent?
Answer
Bela starts with ₹100 and spends ₹5 a day, so after n days she has ₹(100 − 5n).
n = 15: 100 − 5(15) = 100 − 75 = ₹25
The money runs out when the amount left is zero.
100 − 5n = 0
5n = 100
n = 20 days
5n = 100
n = 20 days
Why this is decay, and where it stops: the coefficient of n is −5, so every extra day subtracts a fixed ₹5 — a linear pattern running downwards. The pattern is only meaningful while the amount left is not negative, i.e. while 100 − 5n ≥ 0, that is n ≤ 20. On day 20 the purse is exactly empty; on day 21 the formula would say −₹5, which the situation does not allow. Real-world models carry such limits even when the algebra does not.
Tip: the value at which a linear polynomial becomes 0 is worth naming — here it answers “when does it run out?” in one step.