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17. The number of bacteria, measured in thousands, in a culture is modeled by th...

Apr 29, 2024

17. The number of bacteria, measured in thousands, in a culture is modeled by the equation

b(t)=\frac{380 e^{231 t}}{175+e^{321 t}}

, where

t

is the number of days since the culture was formed. According to this model, the culture can support a maximum population of (A) 2.17 (B) 205 (C) 380 (D) 760 (E)

\infty

That's an interesting question! Let's analyze the given equation for the number of bacteria in the culture:

b(t) = \frac{380 e^{231 t}}{175+e^{321 t}}

To find the maximum population that the culture can support, we need to look at the behavior of the function as

t

approaches infinity. As

t

gets very large, the term

e^{231 t}

will dominate the denominator since it grows much faster than the constant term 175. Therefore, the culture can support a maximum population of 380. So, the correct answer is (C) 380.