The half-life of Kryponite-123 is 40 years. Suppose we have a 700-mg sample. Find the decay k, and the expected amount of Kryptonite left after 30 years.

Question

I need help setting this problem up.

Answer 1

since you are dealing with "half-life" , we can use the formula
amount = c (1/2)^(t/40)
amount = 700 (1/2)^(t/40)
when t = 40, amount = 350

so when t = 30
amount = 700 (1/2)^(30/40)
= 700 (1/2)^.75 = 416.22.. mg

reading your question again, I gather you want to use
amount = 700 e^(kt)

350 = 700 e^(40k)
.5 = e^(40k)
take ln of both sides
ln .5 = 40k
k = ln.5/40 = -.017328...

so when t = 30
amount = 700 e^(30(.017328)) = 416.22.. (same as above)