4 Show your work in detail US Department of Wildlife tagged

4- Show your work in detail .

US Department of Wildlife tagged 100 black- tailed rabbits in a national forest in 2009. in 2010, they tagged 120 black-tailed rabbits in the same range. If the rabbit population follows the uninhibited exponential growth model, how many rabbits will be in the range 5 years from 2009 ?

5- show your work in details

The half-life of Strontium is 30 years. If 50 grams is present now, how much will be present in 50 years ? Round your answer to three decimal places.

Solution

4. We have to use the following formula

A=A₀(1+r)^t

A₀ is the population in 2009 which is 100

120=100 (1+r)

1.2-1=r

r=.2

Therefore rate of growth is 20%=.2

So the population after 5 years will be

A= 100(1+.2)⁵= 100 *1.2⁵=248.8

5. We have to use the following formula

A=A₀(1/2)^t/h

Where A₀ is the initial amount which is 100

h is the half life which is 30 yrs

A=50(1/2)^50/30=15.75 gms