Appendix 2 · Mathematical Modelling

NCERT Class 10 Maths Exercise A2.1

All 1 questions of NCERT Class 10 Maths Exercise A2.1 (Mathematical Modelling), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   Consider the following situation. A problem dating back to the early ​13th century, posed by Leonardo Fibonacci, asks how many rabbits you would have if you started with one pair ​and let them reproduce. Assume that a pair of rabbits produces a pair of offspring each month, and that each pair of rabbits produces their first offspring at the age of $2$ months. Month by month, the number of pairs of rabbits is given by the sum of the pairs in the two preceding ​months, except for the $0$th and the $1$st months. ​The table alongside lists the number of pairs for months $0$ to $16$; after about $16$ ​months you have nearly $1600$ pairs of rabbits. Clearly state the problem and the different stages of ​mathematical ​modelling in this situation.

   Pairs of rabbits month by month (months 0 to 16)

   Month	Pairs of Rabbits
   0	1
   1	1
   2	2
   3	3
   4	5
   5	8
   6	13
   7	21
   8	34
   9	55
   10	89
   11	144
   12	233
   13	377
   14	610
   15	987
   16	1597

   Show answer

   Problem: starting from one pair of rabbits, find the number of pairs present at the end of each month up to month $16$. Stages of modelling: (1) State the problem precisely; (2) Make assumptions (no deaths, one new pair per mature pair per month, maturity at $2$ months); (3) Formulate the recurrence $a_n=a_{n-1}+a_{n-2}$ with $a_0=a_1=1$; (4) Iterate to get $a_{16}=1597$; (5) Interpret and validate against the stated near-$1600$ pairs.

   Step-by-step solution →