Math Half life equations

Question

The half-life of Palladium-100 is 4 days. After 12 days a sample of Palladium-100 has been reduced to a mass of 4 mg. What was the initial mass (in mg) of the sample? 

What is the mass 6 weeks after the start? 

Answer 1

4 = a₀(0.5)^12/4, calculate

a(t) = a₀ (0.5)^28/4, use the value of a₀ from previous

Answer 2

a=4/(1/2)^(12/4)= 32mg

= initial amount

6 weeks = 7x6= 42 days. Half life = 4 days

a(42)=32(1/2)^42/4= about .0221 mg after 6 weeks

t = number of days, a(t) = amount at time t

0 32

4 16

8 8

12 4

16 2

20 1

24 .5

28 .25

32 .125

36 .0625

40 .03125

42 about .0221 mg after 6 weejs

44 .015625