Interactive applet

Linear vs Exponential vs Quadratic

Overlay three models on the same axes and compare how they grow.

Algebra I Regents

Hands-on lab

Compare growth

Linear y = 0.8x + 1 (constant add)Exponential y = 0.6(1.45)^x (constant multiply)Quadratic y = 0.15x² (changing add)

Long-run growth

Exponential growth eventually overtakes both linear and quadratic for these positive rates. Check a table of first differences vs. ratios to classify a data set.

Guided questions

Which graph eventually overtakes the others for large x?

Reflection

Describe a real NYC context that is linear, one that is exponential, and one that is quadratic.