Use the exponential decay model, Upper A equals Upper A 0 e Superscript kt, to solve the following. The half-life of a certain substance is 25 years. How long will it take for a sample of this substance to decay to 60% of its original amount?

18.42 years.

Step-by-step explanation:

We have been that the half-life of a certain substance is 25 years. We are asked to find time taken by substance to decay to 60% of its original amount.

We will use formula to solve our problem.

First of all, we will find value of k using , and .

Now we will take natural log of both sides of equation.

Our function would be .

Now we have and .

Now we will take natural log on both sides.

Therefore, it will take approximately 18.42 years for a sample of this substance to decay to 60% of its original amount

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