Question

Conservationists tagged 120 ​black-nosed rabbits in a national forest in 1990. In 1991​, they tagged 240 ​black-nosed rabbits in the same range. If the rabbit population follows the exponential​ law, how many rabbits will be in the range 9 years from​ 1990?

Answer 1

Answer:

Hence after period of 9 years from 1990 t0 1999 will be 61438 rabbits.

Step-by-step explanation:

Given:

Population for rabbit obeys exponential law.

120 at 1990 and 240 1991 ...after 1 year time period

To Find:

After 9 year  time period how many rabbits will be there.

Solution:

Exponential law goes on present value and various value and time period and defined as ,

let Y be present value Y0 previous year value  and k exponential constant and t be time period.

So

Y=Y0e^(kt)

Here Y=240  ,Y0=120  t=1 year time period

So

240=120e^(k*1)

240/120=e^k

2=e^k

Now taking log on both side, [natural log]

ln(2)=ln(e^k)

ln(2)=kln(e)

k=ln(2)

k=0.6931

For t=9 year of time period

Y0=120,  t=9  ,k=0.6931

Y=Y0e^(k*t)

Y=120*e^(0.6931*9)

=120e^6.2383

=61438.48

=61438 rabbits