Algebra II : Radioactive Decay Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #3451 : Algebra Ii

An element has a half life of 6 days.  What is the approximate amount remaining for a 50 mg sample of this element after 5 days?

Possible Answers:

\displaystyle 1.5625

\displaystyle 48.4375

\displaystyle 28.06155

\displaystyle 21.93845

Correct answer:

\displaystyle 28.06155

Explanation:

Write the formula for half life.

\displaystyle y=a(\frac{1}{2})^x

Since the time requested is five out of the six day of the half life, the value of \displaystyle x is:

\displaystyle x=\frac{5}{6}

Substitute all the known values into the equation.

\displaystyle y=50(\frac{1}{2})^{\frac{5}{6}} = 28.06155

The answer is:  \displaystyle 28.06155

Example Question #791 : Mathematical Relationships And Basic Graphs

The number of butterflies in an exhibit is decreasing at an exponential rate of decay. The number of butterflies is decreasing by \displaystyle 5\% every year. There are \displaystyle 500 butterflies in the exhibit right now. How many butterflies will be in the exhibit in \displaystyle 7years? 

Possible Answers:

\displaystyle 250

\displaystyle 296

\displaystyle 0

\displaystyle 349

Correct answer:

\displaystyle 349

Explanation:

Because the butterflies are decreasing exponentially, we can use this equation

\displaystyle \small F = O\cdot(1-\text{decay})^{\text{time}}

\displaystyle \small F is the final value

\displaystyle \small O is the original value

The decay for this problem is 5% or 0.05

The period of time is 7 years

Using this equation we can solve for \displaystyle \small F

\displaystyle \small F = 500(1-0.05)^7 = 500\cdot0.95^7 \approx 349

\displaystyle \small F = 349

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