Distance between (20,15) and (10,25)
1 answer:
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Answer:
The half-life of the substance is about 288 days.
Step-by-step explanation:
The exponential decay function:
Can determine the amount <em>A</em> of a radioactive substance present at time <em>t. A₀ </em>represents the initial amount and <em>P</em> is the half-life of the substance.
We are given that a substance loses 70% of its radioactivity in 500 days, and we want to determine the period of the half-life.
In other words, we want to determine <em>P. </em>
Since the substance has lost 70% of its radioactivity, it will have only 30% of its original amount. This occured in 500 days. Therefore, <em>A</em> = 0.3<em>A₀</em> when <em>t</em> = 500 (days). Substitute:
Divide both sides by <em>A₀:</em>
We can take the natural log of both sides:
Using logarithmic properties:
So:
Take the reciprocal of both sides:
Use a calculator:
The half-life of the substance is about 288 days.