Given that we know the initial mass of Iodine and its half-life, we want to see how much will remain after 40 days.
After 40 days, 244.17 grams of Iodine will remain.
<h3 /><h3>The half-life of materials and how to use it:</h3>
The half-life of a material is the time it takes for that amount of material to reduce to its half.
We can model the amount of Iodine as:
A(t) = A*e^{k*t}
- Where A is the initial amount, in this case, 7800g.
- k is a constant that depends on the half-life.
- t is the time in days.
Replacing what we know, we get:
A(t) = 7800g*e^{k*t}
Now we use the fact that the half-life is 8 days, this means that:
e^{k*8} = 1/2
ln(e^{k*8}) = ln(1/2)
k*8 = ln(1/2)
k = ln(1/2)/8 = -0.0866
Then the function is:
A(t) = 7800g*e^{-0.0866*t}
So now we just need to evaluate this in t = 40.
A(40) = 7800g*e^{-0.0866*40} = 244.17g
So, after 40 days, 244.17 grams of Iodine will remain.
If you want to learn more about half-life and decays, you can read:
brainly.com/question/11152793
]
