A sample of a radioactive substance decayed to 97% of its original amount after a year. (Round your answers to two decimal places.) (a) What is the half-life of the substance? 22.76 Correct: Your answer is correct. yr (b) How long would it take the sample to decay to 85% of its original amount? yr

The half life of the substance is 22.76 years

Half life is given by:

Given that t = 1 years, N(t) = 97% of normal amount = 0.97N₀. Hence:

a)

b)

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a) The half life of the substance is 22.76 years.

b) 5.34 years for the sample to decay to 85% of its original amount

Step-by-step explanation:

The amount of the radioactive substance after t years is modeled by the following equation:

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

A sample of a radioactive substance decayed to 97% of its original amount after a year.

This means that:

Then

So

(a) What is the half-life of the substance?

This is t for which P(t) = 0.5P(0). So

The half life of the substance is 22.76 years.

(b) How long would it take the sample to decay to 85% of its original amount?

This is t for which P(t) = 0.85P(0). So

5.34 years for the sample to decay to 85% of its original amount