Sodium-24 has a half-life of 15 hours. How much sodium-24 will remain in an 18.0 g sample after 60 hours?
Using
A = 18e^(kt)... where A is the amount after t hours, we have
9 = 18e^(k*15) divide both sides by 18
1/2 = e^(15*k) take the ln of both sides
ln(1/2) = ln e^(15* k) and by a log property, we can write
ln(1/2) = (15k) lne and lne = 1 so we can drop that part
ln(1/2) = 15k divide both sides by 15
k = ln(1/2) / 15 = -.0462
So after 60 hours, we have
A = 18e^(60* -0462) = about 1.126 g
Here's the graph of the situation.....where x = t ....the relevant values are where x ≥ 0
https://www.desmos.com/calculator/wvzugktxmp
Using
A = 18e^(kt)... where A is the amount after t hours, we have
9 = 18e^(k*15) divide both sides by 18
1/2 = e^(15*k) take the ln of both sides
ln(1/2) = ln e^(15* k) and by a log property, we can write
ln(1/2) = (15k) lne and lne = 1 so we can drop that part
ln(1/2) = 15k divide both sides by 15
k = ln(1/2) / 15 = -.0462
So after 60 hours, we have
A = 18e^(60* -0462) = about 1.126 g
Here's the graph of the situation.....where x = t ....the relevant values are where x ≥ 0
https://www.desmos.com/calculator/wvzugktxmp