Final answer:
The percent change in the number of bacteria every second is a 19% decrease, as calculated by the exponential decay function B(t)=6400·(0.81)t/4, which depicts the rapid reduction of bacteria in a petri dish due to a special medicine.
Step-by-step explanation:
The question pertains to the exponential decay of a bacterial population in the presence of a special medicine. Given the function B(t)=6400·(0.81)t/4, we can determine the percent change in the number of bacteria every second by evaluating the base of the exponential function, 0.81.
Since t is in seconds and it appears as t/4 in the exponent, the function represents the number of bacteria after every quarter of a second. To find the percent change per second, we observe that after 4 seconds (which is 4 quarters of a second), the bacteria population is multiplied by 0.814. Since we want to know the percent change each second, we calculate 0.81 to the power of 1, since 4/4 is 1. Therefore, the bacteria multiply by 0.81 each second.
The percent decrease each second is then calculated by subtracting 0.81 from 1 to find the proportion of decrease, and then multiplying by 100 to convert it to a percentage. It results in (1 - 0.81) × 100 = 19%. Thus, the bacteria population decreases by 19% every second due to the medicine.
This model represents an exponential decay which is in contrast to exponential growth that you might study when looking at ideal conditions where resources are unlimited. However, in real situations, environmental factors such as medicine can lead to a rapid reduction in a bacterial population, illustrating an exponential decay scenario.