Solution for Section 8.1 Question 6

6. a) From page 431 of the textbook,  F₁ = 1.

b) From page 431 of the textbook,  F_n = F_n-1 + F_n-2 for all integers n2.

c) To calculate the value of F₂₄ we need all the previous terms. In the textbook the values of F₀ through to F₁₂ appear on page 432.
F₁₃ = F₁₂ + F₁₁ = 377.
F₁₄ = F₁₃ + F₁₂ = 610.
F₁₅ = F₁₄ + F₁₃ = 987.
F₁₆ = F₁₅ + F₁₄ = 1597.
F₁₇ = F₁₆ + F₁₅ = 2584.
F₁₈ = F₁₇ + F₁₆ = 4181.
F₁₉ = F₁₈ + F₁₇ = 6765.
F₂₀ = F₁₉ + F₁₈ = 10946.
F₂₁ = F₂₀ + F₁₉ = 17711.
F₂₂ = F₂₁ + F₂₀ = 28657.
F₂₃ = F₂₂ + F₂₁ = 46368.
F₂₄ = F₂₃ + F₂₂ = 75025.

Assuming that no rabbits die, at the end of two years, there will be 75025 rabbit pairs, that is, 150050 rabbits.

Back to Section 8.1