Question

An unknown radioactive element decays into non-radioactive substances. In 30 days the radioactivity of a sample decreases by 12%. The exponential decay model for the decay after t days is given by P(t)=P0e−0.004261t When will a sample of 50 mg decay to 10 mg? Round your final answer to 1 decimal place.

Answer 1

Answer:

The sample of 50 mg decay to 10 mg in 377.7 time.

Explanation:

Given that:- The exponential decay model for the decay after t days as:-

$[P_t]=[P_0]e^{-0.004261t}$

Where,  

$[P_t]$ is the concentration at time t

$[P_0]$ is the initial concentration

Given:

$[P_0]$ = 50 mg

$[A_t]$ = 10 mg

So,

$10=50e^{-0.004261t}$

$e^{-0.004261t}=\frac{1}{5}$

$t=\frac{\ln \left(5\right)}{0.004261}$

$t=377.7$

The sample of 50 mg decay to 10 mg in 377.7 time.