could anyone explain this to me?
Conservationists tagged 90 black-nosed rabbits in a national forest in 1990. In 1993, they tagged 180 black-nosed rabbits in the same range. If the rabbit population follows the exponential law, how many rabbits will be in the range 5 years from 1990?
Conservationists tagged 90 black-nosed rabbits in a national forest in 1990. In 1993, they tagged 180 black-nosed rabbits in the same range. If the rabbit population follows the exponential law, how many rabbits will be in the range 5 years from 1990?
-
In exponential growth, the quantity at time t from the initial measurement is given by:
Q(t) = Q(0)e^(kt) where k is a constant. In this case we can find k by taking:
Q(3) = Q(0)e^(k3) or
180 = 90*e^(3k)
2 = e^(3k) take the natural log (ln) of both sides
ln(2) = 3k or
k = ln(2)/3 = 0.23104906
Therefore Q(5) = 90e^(0.23104906*5) = 285.732189
So the answer is 285+ black-nosed rabbits in 1995.
Q(t) = Q(0)e^(kt) where k is a constant. In this case we can find k by taking:
Q(3) = Q(0)e^(k3) or
180 = 90*e^(3k)
2 = e^(3k) take the natural log (ln) of both sides
ln(2) = 3k or
k = ln(2)/3 = 0.23104906
Therefore Q(5) = 90e^(0.23104906*5) = 285.732189
So the answer is 285+ black-nosed rabbits in 1995.