9k C log D log 6The halflife of plutonium234 is 9 hours If 8

(9-k) C log, D) log 6.The half-life of plutonium-234 is 9 hours. If 80 milligrams is present now, how much will be present in 3 days? (Round your answer to three decimal places.) A) 45.948 B) 7.936 C) 0312 D) 63.495 7. Conservationists tagged 100 black-nosed rabbits in a national forest in 1990. In 1993, they tagged 200 black-nosed rabbits in the same range. If the rabbit population follows the exponential law, how many rabbits will be in the range S years from 1990? A) 259 B) 635 C) 130 D) 1270 8. Solve the equation: log2 (x) 3 8. Solve the equation: log2 (x)--3 9) What is the sum of the solutions of the equation 9-43+3-0? A)1 B)2 C)3 D) 4

Solution

6) 3 days =3*24=72 hours

number of half lifes =72/9 =8

amount present after k half lifes =80/2^k

amount present after 8 half lifes =80/2⁸

amount present after 8 half lifes =80/256

amount present after 8 half lifes =0.312 milligrams

7)amount after t years y=y_oe^kt

initial amount y_o=100

y=100e^kt

200 rabbits in 1993, t =3

200=100e^k3

e^k3=2

3k=ln2

k=(1/3)ln2

k=0.231

y=100e^0.231t

8 years from 1990, t =8

y=100e^0.231*8

y=635

635 rabbits on 8 years from 1990

8)log₂x =-3

x =2^-3

x =1/8

9)9^x-4.3^x+3=0

3^2x-4.3^x+3=0

(3^x)²-4.3^x+3=0

(3^x)²-3.3^x-3^x+3=0

3^x(3^x-3)-1(3^x-3)=0

(3^x-3)(3^x-1)=0

3^x=3,3^x=1

x =1 , x=0

sum of solutions=1+0=1