MATH SOLVE

3 months ago

Q:
# A gardener brought 5 rabbits, after 2 months rabbits became 10, and after 4 months they became 20. If the growth continues on the same ratio, what would be the amount of rabbits after 1 year?(a) 300 (b) 435(c) 535 (d) 635

Accepted Solution

A:

Answer:Initial population of Rabbit = 5 rabbitAfter 2 monthsPopulation of Rabbit = 10 After 4 months population of rabbit = 20Formula for growth is :G = [tex]G_{0}[1 + R]^n[/tex], where G is final population and [tex]G_{0}[/tex] is initial population, and R is growth rate.1. 10 = 5 [1 +R]²Dividing both sides by 5 , we get2 = (1 + R)²→ R + 1 = √2 ⇒ taking positive root of 2→R = √2 -1Amount of rabbit after 1 year = [tex]20(1 + \sqrt2 -1)^8= 20 \times (\sqrt2)^8= 20 \times 2^4= 20 \times 16= 320[/tex]