Desmos Tricks

Logarithmic Regression

Model learning curves and decelerating growth.

🪵 Log Regression Hack

Paste this when data grows fast then slows down.

y_1 ~ a + b*ln(x_1)

📝 SAT Problem

A Biology student measures bacteria growth over time: \((1, 10), (5, 25), (10, 32)\).

Using a logarithmic model \(y \approx a + b \ln(x)\), what is the predicted count at day 20?

(A) 38
(B) 42
(C) 50
(D) 65

Step 1: Enter the Data

Click + then Table. Type the points: \((1, 10)\), \((5, 25)\), \((10, 32)\).

Step 2: Run the Regression

In a new box, paste the code: y_1 ~ a + b*ln(x_1).

Desmos will calculate a and b instantly.

Logarithmic Regression Desmos Solution

Step 3: The Prediction

To find the value for day 20, type: a + b*ln(20).

Desmos gives: 38.42.

✅ Final Answer: (A)