Answer:
107.00 years
Step-by-step explanation:
You want the time it takes for 2000 grams of radioactive material to decay to 155 grams if the half-life is 29 years.
Exponential decay
The remaining amount of material can be modeled by ...
a = (initial amount)·(1/2)^(t/(half-life))
a = 2000·(1/2)^(t/29)
Solving for t when a=155 gives ...
155/2000 = 1/2^(t/29) . . . . . divide by 2000
log(155/2000) = (t/29)·log(1/2)
29·log(155/2000)/log(1/2) = t ≈ 107.00
There will be 155 grams remaining in 107.00 years.
