Imagine a glass that contains 500ml of water. If 12% of the water evaporates every hour, how long will it take for 100ml to remain?

We can solve this problem using the following equation:

Figure 1. |
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y = final amount

a = initial amount

r = rate of decay

t = time

We can arrange our knowns to solve for the unknown, using the logarithmic properties we learned about recently:

Figure 2. |
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It will take 12.59 hours for 100ml of water to remain.

The half-life of a radioactive substance is the time it will take for half of the substance to decay. For example, the half-life for a mass of Carbon is 5730 years.

We can solve this problem using the following equation:

Figure 3. |
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What is k? That is, what is the rate of decay of Carbon?

y = final amount

a = initial amount

e = natural base

t = time

Again, we can arrange our knowns to solve for the unknown, using the logarithmic properties we learned about recently:

Figure 4. |
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The rate of decay of Carbon is k = .00012