Final answer:
The model B(t) = 8500 ⋅ (0.827)^{t/3} showcases a decline in bacterial numbers due to the application of a medicine, which impacts the rate of exponential growth by introducing a decaying factor less than 1, thus, indicating a negative rate of change in the bacterial population.
Step-by-step explanation:
The model B(t) = 8500 ⋅ (0.827)^{t/3} represents the number of bacteria remaining in a petri dish after introducing a special medicine, which affects the bacteria's exponential growth. Exponential growth in a bacterial population occurs when the resources are unlimited, and the population size increases at an accelerating rate. The concept implies that each generation of bacteria adds more organisms to the population than the previous one. However, in the real world, resources are usually limited, and factors such as the introduction of medicine can lead to a reduction in the growth rate of bacteria.
The rate of change in the context of the bacterial growth model shows how the number of bacteria changes over time. It is affected by both the birth rate and death rate of the bacteria. In the formula given, 0.827 represents the fraction by which the bacteria population is multiplied after every one-third of the unit of time. As the base of the exponent is less than 1, this indicates a decaying population, meaning the rate of change of the bacteria population is negative, as the medicine inhibits their growth or kills them.