Half Life Problem: Solving for 5 Years Starting with 100 Grams

[magnifik]

The problem:
A radioactive material has a half-life of 50ln2 years. If you add 5 grams per year to the material, how much material will you have after 5 years if you start with 100 grams?

What I've done so far:
t = ln2/k = 50ln2
k = 1/50
k = .02
A = A₀e^-kt
N = 100e^(-.02)(5) = 90 grams
90 + 5 = 95 grams

i'm not sure if this is correct because i have a feeling this is not the correct way to take into account the 5 grams per year being added constantly. please let me know if i need to fix anything. thx.

 

[Borek]

Calculate mass after a year, add 5. Repeat five times.

 

[CompuChip]

Perhaps it would be easier if you start by writing down a recursive equation, i.e. express the quantity N(t + 1) after one year in terms of the quantity N(t) in the previous year?

 

[magnifik]

using both suggestions i would have
N(t + 1) = (N(t) e^-kt) + 10
but i would still have to sum up each value from t = 0 to 4
is there an easier way to do this?