The regression equation given for the water lilies is [tex]\( y = 3.915 (1.106)^x \)[/tex]. Let’s break this down to understand what the constants represent in terms of the water lily population change.
1. The value 3.915 represents:
- This value is the initial amount or starting value of the water lily population. It tells us the population size of the water lilies when [tex]\( x \)[/tex] (which could represent time or another variable) is equal to 0. So, at the beginning of the period being studied, there were 3.915 water lilies.
2. The value 1.106 represents:
- This value is the growth rate of the water lily population. It indicates how the population changes over each time period. Specifically, if the population is growing exponentially, this means the population increases by a factor of 1.106 for each unit increase in [tex]\( x \)[/tex]. For example, if [tex]\( x \)[/tex] represents years, then each year, the population of water lilies increases by 10.6%.
Therefore, the initial population of water lilies is 3.915, and the population is growing at a rate of approximately 10.6% per time unit.
