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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