MATH  solving exponential equations
posted by Cyn on .
The halflife of sodium24 is 14.9 hours. A hospital buys a 40 mg sample of sodium24.
a) How many grams, to the nearest tenth, of sodium21 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. ><

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