The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. 5 tarting with 210 grams of a radioactive isotope, how much will be left after 5 half-lives? Use the calculator provided and round your answer to the nearest gram.

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Let $$ m_0 = 210 $$ grams be the initial mass. After each half-life, the mass is reduced to half, so after $$ n $$ half-lives the mass $$ m $$ is given by

$$
m = m_0 \times \left(\frac{1}{2}\right)^n
$$

For $$ n = 5 $$ half-lives, we have

$$
m = 210 \times \left(\frac{1}{2}\right)^5 = 210 \times \frac{1}{32} = \frac{210}{32} \approx 6.5625 \text{ grams}
$$

Rounding to the nearest gram, the mass remaining is

$$
\boxed{7 \text{ grams}}
$$
After 5 half-lives, 7 grams of the radioactive isotope will remain.

The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. 5 tarting with 210 grams of a radioactive isotope, how much will be left after 5 half-lives? Use the calculator provided and round your answer to the nearest gram.

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