Question

A rabbit population doubles every 4 weeks. There are currently five rabbits in a restricted area. If t represents the time, in weeks, and p(t) is the population of rabbits with respect to time, about how many rabbits will be there in 98 days?

Answer 1

98 days = (98 ⁄ 7) weeks = 14 weeks 

Po = initial population = 5 

Ƭ = doubling time in weeks 

t = elapsed time in weeks 

P{t} = population after "t" weeks 


    P{t} = (Po)•2^(t ⁄ Ƭ) 

    P{t} = (Po)•2^(t ⁄ 4) 

    P{t} = 5•2^(t ⁄ 4) 

    P{14} = (5)•2^(14 ⁄ 4)   …   t = 14 weeks = 98 days 

    P{14} = 56   …   population after 14 weeks