Answer:
See explanation below
Step-by-step explanation:
To get this, we need to apply the general expression for half life decay:
N = N₀e(-λt) (1)
Where:
N and N₀ would be the final and innitial quantities, in this case, masses.
t: time required to decay
λ: factor related to half life
From the above expression we need λ and t. To get λ we use the following expression:
λ = t₁₂/ln2 (2)
And we have the value of half life, so, replacing we have:
λ = 8.04 / ln2 = 11.6
Now, we can replace in (1) and then, solve for t:
0.75 = 40 exp(-11.6t)
0.75 / 40 = exp(-11.6t)
ln(0.01875) = -11.6t
-3.9766 = -11.6t
t = -3.9766 / -11.6
t = 0.34 days