Fit an exponential curve to data
Find y = a·b^x for data that grows or shrinks by a steady factor.
Exponential data multiplies by about the same factor each step, like savings that grow by a fixed percentage or a cooling drink. The calculator finds the starting value a and the growth factor b.
The example uses x = 0, 1, 2, 3 and y = 5, 10, 20, 40. It doubles each step, so a = 5 and b = 2.
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 x into L1 and y into L2.
stat10enter1enter2enter3enter▶5enter10enter20enter40enterOpen STAT, move to CALC and choose ExpReg (press 0 to jump to it).
stat▶0Move down to Calculate and press enter.
▼▼▼▼enter
You should seey=a*b^x a=5 b=2
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 x into L1 and y into L2.
data0enter1enter2enter3enter▶▲▲▲▲5enter10enter20enter40enterOpen the STAT menu (2nd then data) and choose ExpReg. Accept the lists with enter.
2ndstatdata5enterenterenter
You should seea=5 b=2
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.
Open Statistics and choose y=a·b^x (use the down arrow to find it in the list, or press 6). Type the x column.
MENU660=1=2=3=Go back to the top, one column right, and type the y column.
▶▲▲▲▲5=10=20=40=ACPress OPTN and choose Regression Calc.
OPTN3
You should seey=a·b^x a=5 b=2
Tips
- All y values must be positive. The calculator takes logarithms behind the scenes.
- The factor b tells you the growth per step. b = 2 means doubling; b = 0.5 means halving.