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-A Radioactive Isotope $\mathrm { X }$ Is a By-Product of Nuclear Fission with a Half-Life Of a By-Product

Multiple Choice

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-A radioactive isotope $\mathrm { X }$ is a by-product of nuclear fission with a half-life of $28.7 \mathrm { yr }$ . After a nuclear accident, large areas surrounding the site were contaminated with isotope X. If 10 micrograms of $X$ is present in a sample, the function $A ( t ) = 10 \left( \frac { 1 } { 2 } \right) ^ { t / 28.7 }$ gives the amount $A ( t )$ , in micrograms, present after $t$ years. Evaluate the function for the given values of $t$ and interpret the meaning in context.
a. $A ( 57.4 ) \quad$ b. $A ( 100 )$

A) a. After $57.4$ years the amount of isotope $X$ is $2.5 \mu \mathrm { g }$ .
b. After 100 years the amount of isotope $X$ is approximately $1.138 \mu \mathrm { g }$ .
B) a. After $57.4$ years the amount of isotope $X$ is $5 \mu \mathrm { g }$ .
b. After 100 years the amount of isotope $X$ is approximately $1.138 \mu \mathrm { g }$ .
C) a. After $57.4$ years the amount of isotope $X$ is $5 \mu \mathrm { g }$ .
b. After 100 years the amount of isotope $X$ is approximately $0.894 \mu \mathrm { g }$ .
D) a. After $57.4$ years the amount of isotope $X$ is $2.5 \mu \mathrm { g }$ .
b. After 100 years the amount of isotope $\mathrm { X }$ is approximately $0.894 \mu \mathrm { g }$ .