The population of rabbits in a national forest is modeled by the formula P=8,600+650 ln(t+1) where "t" is the number of years from the present.

Question

a)How many rabbits are now in the forest
b)Estimate when it will take for the number of rabbits to reach 12,000?
c)Estimate how many rabbits there will be 50 years from now
d)Estimate how many rabbits there will be in 100 years from now.
Please show as much work as possible.

Answer 1

at "present time" t = 0
P = 8600 + 650(ln(1), but ln1 = 0
= 8600

b) 8600 + 650 ln(t+1) = 12000
ln(t+1) = 5.23077
t + 1 = e^5.23077 = 186.9
t = 185.9 years ???? (my math is correct)

c) plug in 50 for t, evaluate
(I got 11,156)

d) same as c, plug in t = 100

Answer 2

thank you very much, it all makes sense now except for a. could you explain how you get that number. I plugged it into a calculator and it is correct but i just don't understand how it works.

Answer 3

a )

Now t = 0

8,600 + 650 ln( t + 1 ) =

8,600 + 650 ln( 0 + 1 )=

8,600 + 650 ln ( 1 ) =

8,600 + 650 * 0 =

8,600 + 0 = 8,600

b )

8,600 + 650 ln( t + 1 ) = 12,000

650 ln( t + 1 ) = 12,000 - 8,600

650 ln( t + 1 ) = 3,400

ln( t + 1 )= 3,400 / 650

ln( t + 1 )= 5.23076923

t + 1 = e ^ 5.23076923

t + 1 = 186.93655

t = 186.93655 - 1 = 185.93655

c )

8,600 + 650 ln( 50 + 1 ) =

8,600 + 650 ln( 51 ) =

8,600 + 650 * 3.93182563 =

8,600 + 2,555.6866595 = 11,155.6866595

Rounded 11,156

d )

8,600 + 650 ln( 100 + 1 ) =

8,600 + 650 ln( 101 ) =

8,600 + 650 * 4.61512 =

8,600 + 2999.828 = 11,599.828

Rounded 11,600

Answer 4

Ohh my gosh, thank you. I was just confused about "a" but the extra information cant hurt. Thank you so much.