MATH SOLVE

4 months ago

Q:
# 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)β56.56

we can't have .56 rabbit so round down or up

about 56 or 57 rabbits in 98 days

[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)β56.56

we can't have .56 rabbit so round down or up

about 56 or 57 rabbits in 98 days