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Trava [24]
3 years ago
10

A certain radioactive isotope has leaked into a small stream. Three hundred days after the​ leak, 3% of the original amount of t

he substance remained. Determine the​ half-life of this radioactive isotope.
Mathematics
1 answer:
sesenic [268]3 years ago
6 0
If the half-life is t, then every t days, the amount of the radioactive isotope will be cut in half.
(1/2)^(number of half-lives) = 3%
number of half-lives = ln(0.03) / ln(0.5)
This gives the number of half-lives as 5.06.
Then 300 days = (5.06)(length of 1 half-life)
length of 1 half-life = 300 / 5.06 = 59.29 days
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Step-by-step explanation:

Our coordinates are (6, 0) and (0, -3).

We can use the formula (y₂-y₁)/(x₂-x₁) to find the slope-intercept form (y=mx+b)

Now, we plug the coordinates into the formula and solve.

(0-(-3))/(6-0)

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=\frac{1}{2}

So, the slope is \frac{1}{2}.

Now, we have to find the y-intercept, which is the point where the line on the graph intersects with the y-axis.

We can find the y-intercept (which is represented by b) by plugging the information we already know into the formula.

We can use either pair of coordinates for the formula, so I'll use (6, 0).

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Now, we can solve.

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Subtract 3 from both sides.

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2 years ago
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Answer:

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4 0
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