Question

A radioactive substance decays at a rate of 6% each year. If the initial amount of the substance was 600 grams, create an exponential function to model the decay of the substance. Which of the following options correctly models the decay?

Option #1: f (x) = 600(0.06)^x
Option #2: f (x) = 600(1.06)^x
Option #3: f (x) = 600(0.6)^x
Option #4: f (x) = 600(0.94)^x

Answer 1

Decay by 6% per year means each year you keep 94% = 1 − 0.06 of the amount. With initial amount 600 g:

f(t) = 600(0.94)^t , where t is years.

So Option #4 is correct.