Answer :
Answer:
t = 1.51
Step-by-step explanation:
Exponential Model
The exponential model is often used to simulate the behavior of a magnitude that either grow or decay in proportion to the existing amount of that magnitude.
The model can be expressed as
[tex]M=M_oe^{kt}[/tex]
In this case, Mo is the initial mass of the radioactive substance and k is a constant which value is positive if the mass is growing or negative if the mass is decaying.
The value of k is not precisely given in the question, we are assuming [tex]k=-0.2[/tex]
The model is now
[tex]M=M_oe^{-0.2t}[/tex]
We are required to compute the time it takes the mass to reach one-half of its initial value:
[tex]\displaystyle \frac{M_o}{2}=M_oe^{-0.2t}[/tex]
Simplifying
[tex]\displaystyle \frac{1}{2}=e^{-0.2t}[/tex]
Taking logarithms
[tex]\displaystyle ln\frac{1}{2}=ln(e^{-0.2t})=-0.2t[/tex]
Solving for t
[tex]\displaystyle t=-\frac{ln\frac{1}{2}}{0.2}=1.51[/tex]