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

a. Write an equation to determine the number of milligrams remaining after t days.
b. How many milligrams are remaining after 45 hours?
c. How long will it be until there are 5 milligrams remaining?

Sodium 24 has a halflife of approximately 15 hours Consider a sample of 100 milligrams a Write an equation to determine the number of milligrams remaining after class=

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Answer:

a) X = 100 × 0.5^(8t/5)

b) 12.5 mg

c) 2.7 days or 64.8 hours

Step-by-step explanation:

Let X be the amount after time t

15 hours = 15/24 days

= ⅝ days is the half life

a) X = 100 × 0.5^(t ÷ ⅝)

X = 100 × 0.5^(8t/5)

b) 45 hours ÷ 24 = 15/8 days

t = 15/8

X = 100 × 0.5^(8/5 × 15/8)

X = 100 × 0.5³

X = 12.5

5 = 100 × 0.5^(8/5 × t)

0.5^(8t/5) =0.05

(8t/5) ln0.5 = ln0.05

8t/5 = 4.321928095

t = 2.701205059 days

Or, 64.82892142 hours

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