Desmos Tricks

Power Regression

Model inverse square laws and geometric geometry.

āš” Power Regression Hack

Use for inverse variation like I = k/dĀ².

y_1 ~ a*x_1^b

šŸ“ SAT Problem

The intensity of a signal is measured at different distances: \((2, 100), (4, 25), (5, 16)\).

Using a power regression \(y \approx ax^b\), what is the intensity at distance 10?

(A) 2
(B) 4
(C) 5
(D) 8

Step 1: Enter the Data

Click + then Table. Type the points: \((2, 100)\), \((4, 25)\), \((5, 16)\).

Step 2: Run the Regression

In a new box, paste the code: y_1 ~ a*x_1^b.

Power Regression Desmos Solution

Step 3: Solve for Distance 10

Type a * 10^b to get the intensity at distance 10.

Desmos calculates: 4.

āœ… Final Answer: (B)