Exponential growth
Find what a quantity grows to at a fixed percentage rate, and how long it takes to double.
If something grows by a fixed percent each period, its size after t periods is start × (1 + rate)^t.
Example: 500 grows 8% a year for 12 years. 500 × 1.08^12 = 1259.085058. The doubling time solves 1.08^t = 2, so t = ln 2 ÷ ln 1.08 = 9.006468342 years.
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 500 × 1.08 ^ 12 and press enter.
500×1.08^12enterFor the doubling time, type ln(2) ÷ ln(1.08) and press enter.
ln2)÷ln1.08)enter
You should see1259.085058 9.006468342
Classic Graphing 84 key reference · Classic Graphing 84 manual
Classic Scientific 30
Start on the main screen: Press 2nd then mode (QUIT) to leave any menu or screen and return to the calculation screen.
Type 500 × 1.08 ^ 12 and press enter.
500×1.08^12enter
You should see1259.085058
Classic Scientific 30 key reference · Classic Scientific 30 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 500 × 1.08, then the power key and 12, and press =.
500×1.08x12=
You should see1259.085058
Natural Scientific 991 key reference · Natural Scientific 991 manual
Natural Color Graphing
Start on the main screen: Press MENU then 1 to open Run-Matrix, the main calculation screen. Press EXIT to back out of a bar or screen, and SHIFT then EXIT (QUIT) to return to the app start.
Type 500 × 1.08, then the power key and 12, and press EXE.
500×1.08^12EXE
You should see1259.085058
Natural Color Graphing key reference · Natural Color Graphing manual
Classic CAS
Start on the main screen: Press home to open the Home menu (Calculator, Graphs, Settings, and more). Choose Calculator, or press esc to go back to the calculation page.
Type 500 × 1.08 ^ 12, press the right arrow to leave the exponent, then ctrl enter.
500×1.08^12▶ctrl≈enter
You should see1259.09
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 1.08 ENTER 12, then press yˣ. This is the growth factor.
1.08ENTER12yˣKey in 500 and press ×.
500×
You should see1,259.0851
RPN Advanced 42
Start on the main screen: Press EXIT (once or twice) to close any menu and return to the plain stack view of Y and X.
Key in 1.08 ENTER 12, then press shift and 1/x for yˣ.
1.08ENTER12⇧yˣ1/xKey in 500 and press ×.
500×
You should seex: 1,259.0851
RPN Power 48
Start on the main screen: Press ON to cancel what you are typing, then use the stack view. Open the MODE or VAR menu any time; the stack is always shown above the menu row.
Key in 1.08 ENTER 12, then press yˣ.
1.08ENTER12yˣKey in 500 and press ×.
500×
You should see1259.08505841
Tips
- Write the percent as a decimal: 8% is 0.08, so the growth factor is 1.08. For decay use 1 minus the rate.
- To find the time for a target amount, use logs: t = ln(target ÷ start) ÷ ln(1 + rate).