Respuesta :
126 years....it takes half of the sample to decay in 63 yrs. then half of the sample remaining, ( half of 50% is 25%) takes another 63 years which would total at 126
The amount of time that it takes a sample to lose 75% of its titanium-44 will be 126 years.
What is a half-life?
The amount of time required for an isotope's radioactivity to decrease to 50% of its initial amount.
The half-life is given as,
[tex]\rm N(t) = N_0 \left ( \dfrac{1}{2} \right)^{\dfrac{t}{t_{1/2}}}[/tex]
Where, N₀ is a initial amount, t is the time, [tex]\rm t_{1/2}[/tex] is the half-life time.
The approximate Half-Life of titanium-44 is 63 years.
Then the amount of time that it takes a sample to lose 75% of its titanium-44 will be
N(t) = (1 – 0.75)N₀ = 0.25N₀
Then the time will be given as,
[tex]\rm 0.25N_0 = N_0 \left ( \dfrac{1}{2} \right)^{\dfrac{t}{63}}\\0.25 = \left ( \dfrac{1}{2} \right)^{\dfrac{t}{63}}\\[/tex]
Take log on both side, we have
log 0.25 = (t / 63) log (1/2)
t / 63 = 2
t = 126 years
More about the half-life link is given below.
https://brainly.com/question/24710827
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