Posted by **Cyn** on Tuesday, December 1, 2009 at 9:16pm.

The half-life of sodium-24 is 14.9 hours. A hospital buys a 40 mg sample of sodium-24.

a) How many grams, to the nearest tenth, of sodium-21 will remain after 48 h?

b) After how long will only 2.5 mg remain?

I don't know how to write the exponential function in order to be able to solve this. ><

- MATH - solving exponential equations -
**Reiny**, Tuesday, December 1, 2009 at 10:28pm
amount = 40(1/2)^(t/14.9) , where t is the number of hours.

test: if t = 0, Amount = 40 , Check!

if t = 14.9

amount = 40(1/2)^1 = 20 , Check!

a) if t = 48

Amount = 40(1/2)^(48/14.9)

= 40(1/2)^3.22147651

= 40(.107210899)

= appr. 4.29 g

b) 2.5 = 40(1/2)^(t/14.9)

.0625 = (.5)^(t/14.9)

t/14.9 = ln.0625/ln.5

t/14.9 = 4

t = 4(14.9) = 59.6 hours

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