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 respect to time about how many rabbits will there be in 98 days
Accepted Solution
A:
doubling formula is this:
[tex]P(t)=P(2)^{\frac{t}{d}}[/tex] where P=initial number of rabbits t=time d=time it takes to doulbe
ok, so 4 weeks is the doubling time so that is 4*7=28 days
we wawnt time=98 and oroiginal number of rabbits is 5 so [tex]P(98)=5(2)^{\frac{98}{28}}[/tex] [tex]P(98)=5(2)^{3.5}[/tex] [tex]P(98)=5(2^3)(\sqrt{2})[/tex] [tex]P(98)=5(8)\sqrt{2}[/tex] [tex]P(98)=40\sqrt{2}[/tex] so P(98)≈56.56 we can't have .56 rabbit so round down or up about 56 or 57 rabbits in 98 days