College

Sodium 24 has a half-life of approximately 15 hours. Consider a sample of 100 milligrams.


Write an equation to determine the number of milligrams remaining after t days. Show all work.

How many milligrams are remaining after 45 hours? Show all work.

How long will it be until there are 5 milligrams remaining? Show all work.

Sodium 24 has a half life of approximately 15 hours Consider a sample of 100 milligrams Write an equation to determine the number of milligrams

Answer :

The decay equation is: N(t) = [tex]N0 * (1/2)^(t/T),[/tex] where N0 is the initial amount, T is the half-life, and t is time.

How to find the milligrams are remaining after 45 hours

For 45 hours, t = 45/24 = 1.875 days.

Plug values into the equation:

N(1.875) = [tex]100 * (1/2)^(1.875/0.625)[/tex]

= [tex]100 * (1/2)^3[/tex] = 12.5 milligrams.

To find when there are 5 milligrams left,

5 = [tex]100 * (1/2)^(t/0.625).[/tex]

Solving for t: t = 0.625 * log2(100/5)

= 0.625 * 4.322 = 2.70 days.

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