The relationship between the elapsed time \( t \), in seconds, and the number of bacteria, \( B_{\text {second }}(t) \), in the petri dish is modeled by the following function: \( B_{\text {second }}(t)=6000 \cdot\left(\frac{15}{16}\right)^{t} \) Complete the following sentence about the rate of change in the number of bacteria in minutes. Round your answer to two decimal places. Every minute, the number of bacteria decays by a factor of
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To understand the decay factor, we first need to interpret the function. The expression \( \left(\frac{15}{16}\right)^{t} \) suggests that every second, the number of bacteria is multiplied by the fraction \( \frac{15}{16} \). Over one minute, which is 60 seconds, the decay factor becomes \( \left(\frac{15}{16}\right)^{60} \). Rounding this calculation to two decimal places gives us the result: every minute, the number of bacteria decays by a factor of approximately 0.35. This decay can represent various real-world scenarios, such as how bacteria might reduce in number due to environmental factors like lack of nutrients or unfavorable conditions. In lab settings or ecological studies, understanding organism decay rates helps researchers manage populations, maintain healthy cultures, or study the impacts of antibiotics on bacterial growth. This information can be critical for developing effective treatments and preserving ecosystems!
