Growth and Decay (1 Viewer)

[UzurOger]

ive been trying too do this question but seem to always screw it up, any help would be appreciated

7. The amount, N grams of radioactive substance is given by N= No e^-kt , where No and k are constants and t is the time in years. In 3 years the radioactive substance decays from 30 grams to 20 grams

A) after how many years does only 30% of the initial amount of the substance remain?

 

[SoulSearcher]

N = N₀e^-kt
When t = 0, N = 30
30 = N₀e⁰
N₀ = 30
When t = 3, N = 20
20 = 30e^-3k
2/3 = e^-3k
-3k = ln(2/3)
k = ln(2/3) / -3
= 0.135155036...
= 0.135 rounded off to 3 dec. pl (always use the unrounded answer until the final answer)
30% of 30 grams is 9 grams
.'. 9 = 30e^-0.135t
0.3 = e^-0.135t
-0.135t = ln 0.3
t = ln(0.3) / -0.135
= 8.90808688... years
= 8.9 years rounded off to one decimal place.

 

[pLuvia]

N=Noe^-kt
No=30
When t=3, N=20
20=30e^-3k
k=-ln(2/3)/3
=0.135..

N=3/10(No)=Noe^-kt
3/10(30)=30e^-kt
9/30=e^-kt
ln(9/30)=-kt [where k=0.135..]
t=8.908..
=9 years

 

[UzurOger]

hmm thanks seems like i have to improve my calculator skills:wave: