Respuesta :
Answer:
[tex]\bf\displaystyle N=3\cdot \left(\frac{1}{2} \right)^{\frac{t}{250} }[/tex]
Explanation:
Half-life means the time require for a radioactive to have half of its particles disintegrated. Therefore it forms a geometric sequence with:
- the 1st Term (U₁) = initial number of particles
- ratio (r) = [tex]\frac{1}{2}[/tex]
- n = multiple of half-life
Therefore, the general formula for the amount left:
[tex]\boxed{N=N_o\cdot \left(\frac{1}{2} \right)^n}[/tex]
where:
- N = amount left
- N₀ = initial amount
- n = multiple of half-life
For t years, it has a multiple of half-life:
[tex]\boxed{n=\frac{t}{T} }[/tex] where, T = half-life
Therefore, we can also write the formula as:
[tex]\boxed{N=N_o\cdot \left(\frac{1}{2} \right)^{\frac{t}{T} }}[/tex]
Now, we can find the formula by substituting the given data:
[tex]\displaystyle N=N_o\cdot \left(\frac{1}{2} \right)^{\frac{t}{T} }[/tex]
[tex]\bf\displaystyle N=3\cdot \left(\frac{1}{2} \right)^{\frac{t}{250} }[/tex]
