Question

compare linear, exponential, and logistic growth.
linear growth\texponential growth\tlogistic growth
growth rate stays roughly constant over time\t○\t○\t○
growth rate initially increases over time but then decreases and eventually reaches zero\t○\t○\t○
growth rate continues increasing over time\t○\t○\t○
occurs when resources are essentially unlimited and the number of reproductive individuals increases\t○\t○\t○
occurs when the number of reproductive individuals doesnt change\t○\t○\t○
occurs when resources are limited\t○\t○\t○

Explanation:

Step1: Recall Linear Growth

Linear growth has a constant growth rate (e.g., \( y = mx + b \), slope \( m \) is constant). So "Growth rate stays roughly constant over time" matches Linear growth. Also, linear growth occurs when the number of reproductive individuals doesn't change (constant rate).

Step2: Recall Exponential Growth

Exponential growth has a growth rate that increases over time (e.g., \( y = a(1 + r)^t \), rate is proportional to current value). It occurs when resources are unlimited (no carrying capacity), so "Growth rate continues increasing over time" and "Occurs when resources are essentially unlimited..." match Exponential growth.

Step3: Recall Logistic Growth

Logistic growth has an initial exponential - like increase, then growth rate decreases as it approaches carrying capacity (limited resources). So "Growth rate initially increases... then decreases..." and "Occurs when resources are limited" match Logistic growth.

Now, we'll mark the circles:

1. "Growth rate stays roughly constant over time": Linear growth (mark the circle under Linear growth).
2. "Growth rate initially increases over time but then decreases and eventually reaches zero": Logistic growth (mark the circle under Logistic growth).
3. "Growth rate continues increasing over time": Exponential growth (mark the circle under Exponential growth).
4. "Occurs when resources are essentially unlimited and the number of reproductive individuals increases": Exponential growth (mark the circle under Exponential growth).
5. "Occurs when the number of reproductive individuals doesn't change": Linear growth (mark the circle under Linear growth).
6. "Occurs when resources are limited": Logistic growth (mark the circle under Logistic growth).

Answer:

The markings are as follows:

• "Growth rate stays roughly constant over time": Linear growth (circle under Linear growth).
• "Growth rate initially increases over time but then decreases and eventually reaches zero": Logistic growth (circle under Logistic growth).
• "Growth rate continues increasing over time": Exponential growth (circle under Exponential growth).
• "Occurs when resources are essentially unlimited and the number of reproductive individuals increases": Exponential growth (circle under Exponential growth).
• "Occurs when the number of reproductive individuals doesn't change": Linear growth (circle under Linear growth).
• "Occurs when resources are limited": Logistic growth (circle under Logistic growth).