Final answer:
The relationship y = 4(0.8)^x is a model of exponential decay because the base of the exponent (0.8) is between 0 and 1. This results in the y-value decreasing as the x-value increases.
Step-by-step explanation:
To determine whether the relationship y = 4(0.8)^x is a model of exponential growth, exponential decay, or neither, we must look at the base of the exponent, which in this case is 0.8. An exponential growth occurs when the base of the power is greater than 1, resulting in the value of y increasing as x increases. Exponential decay is characterized by a base that is between 0 and 1, which causes the value of y to decrease with increasing x. Since 0.8 is between 0 and 1, this equation represents an exponential decay.
Now let's link this concept to real-world phenomena. For instance, when bacteria grow under ideal conditions, they often multiply at an exponential rate. This is because each new generation of bacteria provides even more organisms to reproduce, leading to rapid increases in population size.
However, if we introduced a limiting factor that reduces the reproductive rate, we would observe an exponential decay in the bacterial population, similar to the decay factor in the given equation.