# MATH - solving exponential equations

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. ><

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1. 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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