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A radioactive substance has a half-life of 47 years. (a) Determine its decay constant. (b) What will be left of a 22 kilogram sample after 15 years?

(a) -0.01474781(b) 17.6 kilograms

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 7

Applications of Exponential and Logarithmic Functions

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This question were given that the half life is equal to 47 years for some radioactive substance. First, we want to find the decay constant. You can see the formula written in green. So we know what our half life is. That was given to us to be 47 years. Which is then equal to the natural log of two divided by K K. B. And R decay constant, Solving for K. We have a decay constant which is equal to negative 0.01475. Now we want to find out how much of a 22 kg sample will be left after 15 years. Again, the formula is written in green. So with this ending amount, which I'm just gonna refer to as a which is what we're trying to find Are starting amount was given to us to be this 22 kg sample divided by two and then to the power of end, which is the number of half life. So we have to solve for N. And being this elapsed time that we've had of 15 years, divided by the half lifetime, which is 47 years. And that gives us the number of half lives that have elapsed during this 15 years. To be 0.31915/2 lives. Let's go ahead and do to to that power 0.31915 And just plug that into your calculator. And we get that this ending amount, or a, as I'm referring to it, is 17.6339 kg.

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