Q12 The halflife of plutonium234 is 9 hours If 70 milligrams

Q12. The half-life of plutonium-234 is 9 hours. If 70 milligrams is present now, how much will be present in 6 days? (Round your answer to three decimal places.)
   a. 0.689
   b. 44.096
   c. 0.001
   d. 23.091

Q13. The function f(x) = 1 + 1.6 ln (x+1) models the average number of free-throws a basketball player can make consecutively during practice as a function of time, where x is the number of consecutive days the basketball player has practiced for two hours. After how many days of practice can the basketball player make an average of 6 consecutive free throws?
   a. 24 days
   b. 80 days
   c. 22 days
   d. 78 days

Solution

12) half-life of plutonium-234 is 9 hours. If 70 milligrams is present now, how much will be present in 6 days?

k (decay constant) = 0.693/9 =0.077

A = Aoe^(-kt)

= 70e^(-0.077*6)

= 44.1 gm

13 ) f(x) = 1 + 1.6 ln (x+1)

f(x) =6 solve for x:

6 = 1+ 1.6ln(x +1)

3.125 = ln(x+1)

22.76 = x+1

x = 21.76 = 22 days

Option c