The half life of substance A is 15 years (i.e after 15 years, you have half of t
ID: 3016713 • Letter: T
Question
The half life of substance A is 15 years (i.e after 15 years, you have half of the amount of substance A that you started with), and substance B decreases by 40 % in 10 years. (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 B in the long term. B. There is less of substance A in the long term. C. There is no way to tell.Explanation / Answer
a) initial amount = 100 mg
so we can write the equation
P = Po e^rt
50 = 100 e^r(15)
1/2 = e^r(15)
r = -0.0462
function for substance A can be written as
f(t) = 100 e^ -0.0462 t
b) function for substance B
P = 100 e^rt
in 10 years 40% decreases
60 = 100 e^10r
60/100 = e^10r
r = -0.05108
g(t) = 100 e^-0.05108 t
c) there is less of substance B in the long term
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