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Ortiz Romero

05/13/2023 · High School

Strontium-90 \( ( ^ { 90 } Sr \) ) is a by-product of nudear fission with a halk-life of approximately \( 28.9 yr \) . After the chernobyl nudear reactor accident in 1986, large areas surrounding the site were contaminated with \( { } ^ { 90 } Sr \) . If \( 5 \mu \) (micrograms) of \( { } ^ { 90 } Sr \) is present in a sample, the function \( A ( t ) = 5 ( \frac { 1 } { 2 } ) ^ { \frac { t } { 28.9 } } \) gives the amount \( A ( t ) \) (in \( \mu g\) )present after t years. Evaluate the function for the given values of \( t \) and interpret the meaning in context. Round to 3 decimal places if necessary. 

 

(a) \( A ( 173.4 ) \) 

(b) \( A ( 57.8 ) \) 

(c) \( A \) (289) 

Answer
expertExpert-Verified Answer

Hobbs Burton
Experienced Tutor
5.0 (45votes)

(a) After 173.4 years, only about 0.078 micrograms of the original 5 micrograms of Strontium-90 will remain.

(b) After 57.8 years, 1.25 micrograms will remain, showing significant decay but still a substantial amount compared to the initial quantity

(c) After 289 years, approximately 0.005 micrograms of 90Sr will remain from the original 5 micrograms.

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