HELP ME PLEASE The half-life of Palladium-100 is 4 days. After 12 days a sample of Palladium-100 has been reduced to a mass of 2 mg.

What was the initial mass (in mg) of the sample?

What is the mass 5 weeks after the start?

The initial mass of the sample was 16 mg.

The mass after 5 weeks will be about 0.0372 mg.

Step-by-step explanation:

We can write an exponential function to model the situation.

Let the initial amount be A. The standard exponential function is given by:

Where r is the rate of growth/decay.

Since the half-life of Palladium-100 is four days, r = 1/2. We will also substitute t/4 for t to to represent one cycle every four days. Therefore:

After 12 days, a sample of Palladium-100 has been reduced to a mass of two milligrams.

Therefore, when x = 12, P(x) = 2. By substitution:

Solve for A. Simplify:

Simplify:

Thus, the initial mass of the sample was:

5 weeks is equivalent to 35 days. Therefore, we can find P(35):

About 0.0372 mg will be left of the original 16 mg sample after 5 weeks.

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step-by-step explanation: