Answer :

facundo3141592

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.

The half-life of materials and how to use it:

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:

https://brainly.com/question/11152793

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