Question

match each population growth model to the graph that best represents it.
linear growth exponential growth logistic growth

Explanation:

1. First graph (left): Calculate the difference between consecutive population values:

• From t=0 to t=3: $10-5=5$
• t=3 to t=6: $15-10=5$
• t=6 to t=9: $20-15=5$
• t=9 to t=12: $25-20=5$
• t=12 to t=15: $40-25=15$
• t=15 to t=18: $70-40=30$

The growth rate increases over time, which is characteristic of exponential growth.

1. Second graph (middle): Calculate the difference between consecutive population values:

• t=0 to t=3: $30-0=30$
• t=3 to t=6: $90-30=60$
• t=6 to t=9: $200-90=110$
• t=9 to t=12: $280-200=80$
• t=12 to t=15: $300-280=20$
• t=15 to t=18: $300-300=0$

Growth starts slow, accelerates, then slows until it reaches a carrying capacity, which is logistic growth.

1. Third graph (right): Calculate the difference between consecutive population values:

• t=0 to t=3: $5-2=3$
• t=3 to t=6: $8-5=3$
• t=6 to t=9: $11-8=3$
• t=9 to t=12: $14-11=3$
• t=12 to t=15: $17-14=3$
• t=15 to t=18: $20-17=3$

The population increases by a constant amount each interval, which is linear growth.

Answer:

• Left graph: exponential growth
• Middle graph: logistic growth
• Right graph: linear growth