# Exponential decay: Half-life

### Exponential decay: Half-life

In the field of nuclear physics, half-life refers to the amount of time required for radioactive substances to decay into half. In this lesson, we will work on word questions about exponential decay of radioactive substances.

#### Lessons

exponential growth/decay: ${ A_f = A_i (f)^{time\over period}}$

${A_f}$: final amount
${A_i}$: initial amount
${f }$
: growth/decay factor
half-time$\to f = {1\over 2}$
triple
$\to f = {3}$
ten-fold
$\to f = {10}$
increase by 10%$\to f = {({1 + {10\over 100}}) } { = 1.1}$
decrease by 8%$\to f = {({1 - {8\over 100}}) } { = 0.92}$
${time}$ : total time given
${period}$ : every length of time
• 1.
half-life decay

Strontium-90 is a radioactive substance with a half-life of 28 days.
How many days will it take for a 200 gram sample of strontium-90 to be
reduced to 8 grams?