Question

The function f(h)=m(1/2)^h gives the mass, m, of a radioactive substance remaining after h half-lives. Iron has a half-life of 2.7 years. Which equation gives the mass of a 200 mg Iron sample remaining after y years, and approximately how many milligrams remain after 12 years?

1: f(x) = 2.7(0.5)200; 1.7 mg
2: f(x) = 200(0.5)12; 30.8 mg
3: f(x) = 200(0.5)12; 30.8 mg
4: f(x) = 200(0.185)12; 3.2 mg
5: f(x) = 200(0.774)12; 9.2 mg

Answer 1

If a certain initial amount, A₀, of material decays with a half-life of h, the amount of material that remains at time t is given by the exponential decay model

$A(t) = A_{0} ( \frac{1}{2} )^{ \frac{t}{h} }$

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Part (a)
Which equation gives the mass of a 200 mg Iron sample remaining after y years?

∴ A₀ = 200 mg , t = y  and   h = 2.7 years
so, the equation will be:

∴ $f(y) =200( \frac{1}{2} )^{ \frac{y}{2.7} }$

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Part (b):
How many milligrams remain after 12 years?


By substitute with y = 12 in the equation obtained from (a)
∴ $f(12) =200( \frac{1}{2} )^{ \frac{12}{2.7} } \\ f(12) = 200( (\frac{1}{2})^{ \frac{1}{2.7} } )^{12} \\ f(12)= 200(0.774)^{12} \\ f(12) = 200 * 0.046 \\ f(12) = \framebox{9.2} \ mg$


So, the correct answer is option ⇒ 5: f(x) = 200(0.774)^12; 9.2 mg

Answer 2

Answer:

The answer is D

Step-by-step explanation: