Question

The half-life of cesium-137 is 30 years. Suppose we have a \( 130 \mathrm{mg} \) sample. (a) Find the mass (in \( \mathrm{mg} \) ) that remains after \( t \) years. \[ y(t)= \] \( \square \) \( \mathrm{mg} \) (b) How much of the sample (in \( \mathrm{mg} \) ) remains after 130 years? (Round your answer to two decimal places.) \( \square \) \( \mathrm{mg} \) (c) After how many years will only \( 1 \mathrm{mg} \) remain? (Round your answer to one decimal place.) \( t= \) \( \square \) \( \mathrm{yr} \)

          The half-life of cesium-137 is 30 years. Suppose we have a \( 130 \mathrm{mg} \) sample.
(a) Find the mass (in \( \mathrm{mg} \) ) that remains after \( t \) years.
\[
y(t)=
\]
\( \square \) \( \mathrm{mg} \)
(b) How much of the sample (in \( \mathrm{mg} \) ) remains after 130 years? (Round your answer to two decimal places.)
\( \square \) \( \mathrm{mg} \)
(c) After how many years will only \( 1 \mathrm{mg} \) remain? (Round your answer to one decimal place.)
\( t= \) \( \square \) \( \mathrm{yr} \)

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The half-life of cesium-137 is 30 years. Suppose we have a 130 mg sample.
(a) Find the mass (in mg ) that remains after t years.

y(t)=

□ mg
(b) How much of the sample (in mg ) remains after 130 years? (Round your answer to two decimal places.)
□ mg
(c) After how many years will only 1 mg remain? (Round your answer to one decimal place.)
t= □ yr

Added by Sheila S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Matthew Elliott

Step 1

Step 1: To find the mass that remains after \( t \) years, we use the formula for exponential decay, which is given by: \[ y(t) = y_0 \cdot \left(\frac{1}{2}\right)^{\frac{t}{T}} \] where \( y_0 \) is the initial mass, \( T \) is the half-life of the substance, and Show more…

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The half-life of cesium-137 is 30 years. Suppose we have a \( 130 \mathrm{mg} \) sample. (a) Find the mass (in \( \mathrm{mg} \) ) that remains after \( t \) years. \[ y(t)= \] \( \square \) \( \mathrm{mg} \) (b) How much of the sample (in \( \mathrm{mg} \) ) remains after 130 years? (Round your answer to two decimal places.) \( \square \) \( \mathrm{mg} \) (c) After how many years will only \( 1 \mathrm{mg} \) remain? (Round your answer to one decimal place.) \( t= \) \( \square \) \( \mathrm{yr} \)

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