Question

the amount of radioactive isotope decays in half every year. the amount of isotope can be modeled f(x)=346(1/2)^x and f(1)=173. what does the 346 represent?

Answer 1

Answer with explanation:

Decay Formula is given by:

       $f(x)=I_{0}(1+\frac{R}{100})^t$

$I_{0}=\text{Initial Amount of radioactive isotope }$

R=Rate at which radioactive isotope is decaying.

t=Time Constant

Now, Coming to the Question ,

The Rate at which  radioactive isotope is decaying is given by the formula:

 $f(x)=346\times[\frac{1}{2}]^x \\\\f(1)=346 \times \frac{1}{2}\\\\f(1)=173\\\\f(0)=346\times[\frac{1}{2}]^0\\\\f(0)=346 \times 1=346$

⇒346= Initial Amount of Radioactive Isotope

 

Answer 2

The 346 is the original mass  of the radioactive isotope.