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Jennifer did an experiment to study the growth rate of bacteria. She examine abacterial culture under the microscope at regular intervals and recorded herobservations in the following table:Time5 10 15 20 25 30(minutes)Bacteria302 424 595 834 11711642CountUse your graphing calculator to determine:. the exponential regression function that approximates the bacteria count, B(t)after t minutesthe bacteria count at the very beginning of the experiment.the growth rate of the bacteria to the nearest whole percento

Jennifer did an experiment to study the growth rate of bacteria. She examine abacterial-example-1
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eThe table of the observation is shown below:

Using a graphing calculator, the graph is plotted as shown below:

QUESTION 1:

The regression function that models the results can be gotten by checking the parameters of the graph as provided by the graphing calculator. These are shown below:

If the general form of an exponential function is given to be:


y=a(b)^x

From the parameter. we have:


\begin{gathered} a=211 \\ \text{and} \\ b=1.07 \end{gathered}

Therefore, the regression function will be:


y=211(1.07)^x

QUESTION 2:

The bacteria count at the beginning of the experiment can be gotten at x = 0. Therefore, we make this substitution into the regression function:


\begin{gathered} At\text{ }x=0 \\ y=211(1.07)^0 \\ y=211*1 \\ y=211 \end{gathered}

Therefore, the bacteria count will be 211.

QUESTION 3:

The growth rate in an exponential function is represented by r, if the function is given to be:


y=a(1+r)^x

Comparing with the equation we used above, we have that:


\begin{gathered} b=1+r \\ \therefore \\ r=b-1 \end{gathered}

Substituting for b = 1.07, we have:


\begin{gathered} r=1.07-1 \\ r=0.07 \end{gathered}

In percent, the rate will be:


\begin{gathered} r=0.07*100 \\ r=7 \end{gathered}

The growth rate is 7%.

Jennifer did an experiment to study the growth rate of bacteria. She examine abacterial-example-1
Jennifer did an experiment to study the growth rate of bacteria. She examine abacterial-example-2
Jennifer did an experiment to study the growth rate of bacteria. She examine abacterial-example-3
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