Question

compare linear, exponential, and logistic growth.

	linear growth	exponential growth	logistic growth
growth rate initially increases over time but then decreases and eventually reaches zero	◯	◯	◯
growth rate continues increasing over time	◯	◯	◯
occurs when resources are essentially unlimited and the number of reproductive individuals increases	◯	◯	◯
occurs when the number of reproductive individuals doesnt change	◯	◯	◯
occurs when resources are limited	◯	◯	◯

Explanation:

Step1: Recall growth type definitions

• Linear growth: Constant rate (slope), reproductive individuals constant. Formula: \( y = mx + b \), rate \( m \) constant.
• Exponential growth: Rate increases (unlimited resources, more reproducers). Formula: \( y = a(1 + r)^x \), rate \( r \) leads to increasing growth.
• Logistic growth: Rate increases then decreases (limited resources), approaches carrying capacity (growth rate → 0). Formula: \( y=\frac{K}{1 + e^{-r(x - x_0)}} \), growth rate peaks then falls.

Step2: Match each row to growth types

1. Growth rate stays roughly constant over time: Linear (constant slope/rate).
2. Growth rate initially increases then decreases to zero: Logistic (S - curve, growth rate peaks then drops as resources limit).
3. Growth rate continues increasing over time: Exponential (unlimited resources, growth accelerates).
4. Occurs when resources are unlimited, reproductive individuals increase: Exponential (no resource limits, more reproducers → faster growth).
5. Occurs when reproductive individuals don’t change: Linear (constant number of reproducers → constant growth rate).
6. Occurs when resources are limited: Logistic (limited resources → growth slows, reaches carrying capacity).

Answer:

Description	Linear growth	Exponential growth	Logistic growth
Growth rate initially increases then decreases to zero	❌	❌	✔️
Growth rate continues increasing over time	❌	✔️	❌
Occurs when resources are unlimited, reproductive individuals increase	❌	✔️	❌
Occurs when reproductive individuals don’t change	✔️	❌	❌
Occurs when resources are limited	❌	❌	✔️

(Mark the circles as per the table: Linear for row 1,5; Exponential for row 3,4; Logistic for row 2,6)