Work out radioactive decay with half-life
Find how much of a sample is left after some time, using N = N₀ × (1/2)^(t/T).
After each half-life T, half of the sample is left. After a time t, the fraction left is (1/2) raised to the power t/T.
Example: 80 g of a substance with a half-life of 5 days. After 12 days: 80 × 0.5^(12 ÷ 5) = 80 × 0.5^2.4 ≈ 15.16 g.
Classic Graphing 84
Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.
Type the starting amount 80 ×, then .5, the power key, and the exponent in brackets: 12 ÷ 5.
80×.5^(12÷5)Press enter.
enter
You should see15.15716567
Classic Graphing 84 key reference · Classic Graphing 84 manual
Natural Scientific 991
Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.
Type 80 × .5, then the power key and the exponent in brackets: 12 ÷ 5. Without the brackets the power would stop after the 12.
80×.5x(12÷5)=
You should see15.15716567
Natural Scientific 991 key reference · Natural Scientific 991 manual
RPN Scientific 15
Start on the main screen: There is no menu to leave. Press the back arrow to clear a number you are typing, or CLx (g then back arrow) to clear the X register.
Key in the base .5 and ENTER. Then calculate the exponent: 12 ENTER 5 ÷ .
.5ENTER12ENTER5÷Press yˣ to raise .5 to that power, then key in 80 and press ×.
yˣ80×
You should see15.1572
Tips
- Whole numbers of half-lives are easy to check: after 3 half-lives you have 1/8 left.
- The time and the half-life must be in the same unit (days and days).