Desmos Tricks

Logistic Growth

Model populations with a carrying capacity (S-curve).

🦠 Logistic Regression Hack

Use this complex code when growth levels off.

y_1 ~ c / (1 + a*e^(-b*x_1))

📝 SAT Problem

The population of deer in a reserve is tracked over years: \((0, 50), (2, 120), (5, 280), (10, 390)\).

If the population follows a logistic growth model, what is the carrying capacity \(c\) (the maximum limit)?

(A) 400
(B) 420
(C) 500
(D) 600

Step 1: Enter the Data

Click + then Table. Type: \((0, 50)\), \((2, 120)\), \((5, 280)\), \((10, 390)\).

Step 2: Run the Regression

Paste the code: y_1 ~ c / (1 + a*e^(-b*x_1)).

Logistic Regression Desmos Solution

Step 3: Find the Capacity

Look at the value of c in the parameter list.

Desmos shows c ≈ 400. That's your limit.

✅ Final Answer: (A)