Question

determine whether the data in the tables below represent exponential or logistic growth
year population size
2012 5
2013 25
2014 125
2015 185
2016 205
exponential growth
logistic growth

Explanation:

Step1: Check exponential - growth ratio

For exponential growth, the ratio of consecutive population sizes should be constant. $\frac{25}{5}=5$, $\frac{125}{25} = 5$, but $\frac{185}{125}=1.48$, $\frac{205}{185}\approx1.11$. The ratio is not constant.

Step2: Check logistic - growth characteristics

Logistic growth has an initial rapid increase followed by a slow - down as it approaches a carrying capacity. Here, the population initially grows rapidly ($5$ to $25$ to $125$) and then the growth rate slows down (from $125$ to $185$ to $205$), which is characteristic of logistic growth.

Answer:

Logistic growth