The starting amount of radioactive iodine-131 was 250 g. The half-life is 8 days. When Leslie measured the amount, she measured 15.625 g of radioactive iodine. How many days have elapsed between measurements?

Approximately days.

Explanation:

Let be the number of iodine-131 half-lives between the two measurements. If the original mass of iodine-131 in this sample is , the mass of iodine-131 in this sample after half-lives would be:

.

In this question, while . The number of half-lives between the two measurements is unknown. The equation would then become:

.

Rearrange this equation to obtain:

.

Apparently, both sides of this equation are positive. There are two ways to solve this equation.

Take the natural log of both sides of this equation:

.

The right-hand side could be rewritten as the following:

.

Therefore:

.

Take the reciprocal of both sides of this equation:

.

Note that the left-hand side is approximately , which is the fourth power of . Therefore, .

Either way, it can be concluded that . Since each iodine-131 half-life is days, of these half-lives would be approximately days. Therefore, approximately days have elapsed between the two measurements.

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pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y