Value of constant 'k' = -0.041097
     Equation modeling the exponential decay → [tex]\text{ln}\frac{N}{N_0}=-0.41097t[/tex]
Rule for the radioactive decay:
- Rule for the radioactive decay is given by the expression,
     [tex]\text{ln}\frac{N}{N_0}=-kt[/tex]
     Here, N = Amount remaining after 't' years
          N₀ = Initial amount of the radioactive element
          k = Constant
          t = Period of decay
Given in the question,
- N = 100 gms
- Nâ‚€ = 75 gms
- Â t = 5 years
Substitute these values in the expression for the value of 'k',
[tex]\text{ln}\frac{75}{100}=-7k[/tex]
[tex]k=\frac{1}{7}[(\text{ln}(75)-\text{ln}(100)][/tex]
[tex]k=\frac{1}{7}[4.317488-4.605170][/tex]
k = -0.041097
Equation modeling the exponential decay → [tex]\text{ln}\frac{N}{N_0}=-0.41097t[/tex]
 Therefore, value of constant 'k' = -0.041097
        Equation modeling the exponential decay → [tex]\text{ln}\frac{N}{N_0}=-0.41097t[/tex]
Learn more about the radioactive decay here,
https://brainly.com/question/9660135?referrer=searchResults
