The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t and has a half-life of 3.3 hours. If 1 gram of this isotope is present initially, how long will it take for 90% of the lead to decay? (Round your answer to two decimal places.)

It will take 10.96 hours for 90% of the lead to decay.

Step-by-step explanation:

The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t

This means that the amount can be modeled by the following function:

In which A(0) is the initial amount and r is the decay rate.

Has a half-life of 3.3 hours.

This means that . We use this to find r.

So

How long will it take for 90% of the lead to decay?

This is t for which , that is, 100 - 90 = 10% of the initial amount.

It will take 10.96 hours for 90% of the lead to decay.

answer: 298143

step-by-step explanation:

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