The half life of substance A is 18 years, and substance B decays at a rate of 30
ID: 3039464 • Letter: T
Question
The half life of substance A is 18 years, and substance B decays at a rate of 30% each decade. (a) Find a formula for a function f(t) that gives the amount of substance A, in milligrams, left after t years, given that the initial quantity was 100 milligrams. f(t) = help (formulas) (a) Find a formula for a function g(t) that gives the amount of substance B, in milligrams, left after t years, given that the initial quantity was 100 milligrams. g(t) = help (formulas) (c) Of which substance is there less in the long term? A. There is less of substance A in the long term. B. There is less of substance B in the long term. C. There is no way to tell.Explanation / Answer
a) half life = 18 years
decays rate = 30% each decade
P = Po e^rt
50 = 100 e^ (r 18 )
1/2 = e^18r
r = - .0385
formula is
f(t) = 100 e^-.0385 t
b) formula for substance B
P = Po e^rt
decays at 30% each decade
70 = 100 e^r(10)
70 / 100 = e^ 10r
formula is
g(t) = 100 e^ - 0.0356t
c) decay rate of substance B is more so substabce B is less in long term
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