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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