Please help me with this

Question

A certain radioactive isotope has leaked into a small stream. Two hundred days after the​ leak, 4​%

of the original amount of the substance remained. Determine the​ half-life of this radioactive isotope.

Answer 1

This is an example of exponential decay. If the half-life in days is T, you can model this situation as

a(t) = a₀ (0.5)^t/T

t = elapsed time in days

a(t) = percent remaining at time t

a₀ = initial percent = 100

T = half-life in days

a(200) = 4

Withe the given information,

a(200) = 100 (0.5)^200/T

4 = 100 (0.5)^200/T

0.04 = (0.5)^200/T

log(0.04) = (200/T) log(0.5)

Can you solve for T and finish from here? You can use any base for the logs, as long as they are both in the same base.