Expo Half

math expo reg help plz

1.The half-life of sodium is 14.9 h. If you buy a 40-mg sample of sodium.
a.Write a function that describes the amount of sodium left at any given time.

Radioactive elements have a half-life. The half life of any given element is the time that is required for one half of the sample to decay. So if you have 10 grams of a radioactive element, after one half-life there will be 5 grams of the radioactive element left. After another half-life, there will be 2.5 g of the original element left, after another half-life, 1.25 g will be left. The equation for half-life calculations is as follows:

A_E = A_o x (0.5) ^ { t / t_(1/2) }

where: A_E is the amount of substance left
………. A_o is the original amount of substance
………. t is the elasped time
………. t_(1/2) is the half-life of the substance

So…. your problem, you know that t_(1/2) = 14.9 h ….. you also know that A_o = 40 mg

The general formula after plugging in the given info changes to….

A_E = 40 x (0.5) ^ { t / (14.9) } ….. Answer for Question 1a.

For Part B, they want you to find the amount of sodium remaining after 48 hours….. So they want you to find A_E when t = 48 h …. All you have to do is substitute the “t” in the formula… with “48″

So….

A_E = 40 x (0.5) ^ { (48) / (14.9) }

Now it’s just math….

48 / 14.9 = 3.221 …. So that means you now have….

A_E = 40 x (0.5)^(3.221) = 40 x 0.107 = 4.288435….. mg

They want you to give your answer in milligrams, rounded to the nearest tenth…. So 4.288435 rounded to the nearest tenth is 4.3

So the answer is….. 4.3 mg of sodium will remain after 48 hours.

HOPE THIS HELPS!

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