Question

The amount of a radioactive isotope decays in half every year. The amount of the isotope can be modeled by f(x) = 346(one half)x and f(1) = 173. What does the one half represent?
A)The starting amount of the isotope
B) The amount of the isotope after one year
C) The rate the isotope decreases
D) The number of years that have passed

Answer 1

Exponential decay formula is :

$y=ab^x$

Where a≠0, b≠1 , b represent growth or decay factor (or rate) and x is any real number.

But if a radioactive isotope decays in half every year which means the decay factor or decay rate is 50% or $\frac{1}{2}$.

So, the formula for half decay will be:

$y=a(\frac{1}{2} )^x$

Where $\frac{1}{2}$ represent c) The rate of isotope decreases.