$\"\"$ Exponential growth and Decay model:

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If $\"\"$ is a differentiable function of $\"\"$ such that $\"\"$ and $\"\"$ for some constant $\"\"$ , then $\"\"$ .

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$\"\"$ is the initial value of $\"\"$ and $\"\"$ is the propotional constant. Exponential growth occurs when $\"\"$ , and exponential decay occurs when $\"\"$ .

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$\"\"$

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Find value of $\"\"$ .

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$\"\"$

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The isotope $\"\"$ has half life $\"\"$ .

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Since the half life of radioactive isotope the value $\"\"$ is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$ . $\"\"$

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The amount of radioactive isotopes after $\"\"$ is $\"\"$ .

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in the above equation.

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$\"\"$

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Initial amount of radioactive isotopes is $\"\"$ .

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$\"\"$

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Find the amount of radioactive isotopes after $\"\"$ .

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in the above equation.

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$\"\"$

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$\"\"$ .

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Amount of radioactive isotopes after $\"\"$ is $\"\"$ .

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$\"\"$

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Initial amount of radioactive isotopes is $\"\"$ .

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Amount of radioactive isotopes after $\"\"$ is $\"\"$ .