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The number of bacteria in a culture is increasing according to the law of exponential growth. There are 105 bacteria in the culture after 2 hours and 325 bacteria after 4 hours. (a) Find the initial population. (Round your answer to the nearest whole number.) bacteria (b) Write an exponential growth model for the bacteria population. Let t represent the time in hours. y

Respuesta :

Manetho

Answer:

a) 45 bacteria

b) 12.27 hours

Step-by-step explanation:

\begin{aligned}

&105=C e^{2 k} \rightarrow C=\frac{125}{e^{2 k}} \rightarrow C=125 e^{-2 k}\\

&325=C e^{4 k}\\

&325=\left(125 e^{-2 k}\right) e^{4 k}\\

&325 / 125=e^{2 k}\\

&\ln (2.8)=2 k\\

&(\ln (2.8)) / 2=k\\

&k \approx .51481\\

&\begin{array}{l}

105=C e^{51481 *} \\

\frac{125}{e^{1.0396}}=C \\

C \approx 45

\end{array}\\

&B=45 e^{51481×(8)}\\

&B \approx 2765.95 \approx 2766\\

&25,000=45 e^{515 t}\\

&\frac{25,000}{45}=e^{.515 t}\\

&\ln \left(\frac{25,000}{45}\right)=.515 t\\

&\ln \frac{25,000}{45} / .515=t

\end{aligned}

t= 12.27 hours

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