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A bacterial culture starts with 207 bacteria and doubles in size every 7.5 hours. Write a model for the number of bacteria after \(\displaystyle t\) hours.

Since the population dobules every 7.5 hours the function must contain the points \(\displaystyle (0,207), (1, 414)\), and \(\displaystyle (2,828)\). This gives a factor of \(\displaystyle 2^\frac{2 t}{15}\). The model is \(\displaystyle P=207\cdot 2^\frac{2 t}{15}\).

Download \(\LaTeX\) 

\begin{question}A bacterial culture starts with 207 bacteria and doubles in size every 7.5 hours. Write a model for the number of bacteria after $t$ hours. 
    \soln{9cm}{Since the population dobules every 7.5 hours the function must contain the points $(0,207), (1, 414)$, and $(2,828)$. This gives a factor of $2^\frac{2 t}{15}$. The model is $P=207\cdot 2^\frac{2 t}{15}$. }

\end{question}

Download Question and Solution Environment\(\LaTeX\)
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HTML for Canvas 
<p> <p>A bacterial culture starts with 207 bacteria and doubles in size every 7.5 hours. Write a model for the number of bacteria after  <img class="equation_image" title=" \displaystyle t " src="/equation_images/%20%5Cdisplaystyle%20t%20" alt="LaTeX:  \displaystyle t " data-equation-content=" \displaystyle t " />  hours. </p> </p>
HTML for Canvas
<p> <p>Since the population dobules every 7.5 hours the function must contain the points  <img class="equation_image" title=" \displaystyle (0,207), (1, 414) " src="/equation_images/%20%5Cdisplaystyle%20%280%2C207%29%2C%20%281%2C%20414%29%20" alt="LaTeX:  \displaystyle (0,207), (1, 414) " data-equation-content=" \displaystyle (0,207), (1, 414) " /> , and  <img class="equation_image" title=" \displaystyle (2,828) " src="/equation_images/%20%5Cdisplaystyle%20%282%2C828%29%20" alt="LaTeX:  \displaystyle (2,828) " data-equation-content=" \displaystyle (2,828) " /> . This gives a factor of  <img class="equation_image" title=" \displaystyle 2^\frac{2 t}{15} " src="/equation_images/%20%5Cdisplaystyle%202%5E%5Cfrac%7B2%20t%7D%7B15%7D%20" alt="LaTeX:  \displaystyle 2^\frac{2 t}{15} " data-equation-content=" \displaystyle 2^\frac{2 t}{15} " /> . The model is  <img class="equation_image" title=" \displaystyle P=207\cdot 2^\frac{2 t}{15} " src="/equation_images/%20%5Cdisplaystyle%20P%3D207%5Ccdot%202%5E%5Cfrac%7B2%20t%7D%7B15%7D%20" alt="LaTeX:  \displaystyle P=207\cdot 2^\frac{2 t}{15} " data-equation-content=" \displaystyle P=207\cdot 2^\frac{2 t}{15} " /> . </p> </p>