Question

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

Answer 1

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:

$\begin{gathered} At\text{ }x=0 \\ y=211(1.07)^0 \\ y=211\times1 \\ y=211 \end{gathered}$

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:

$\begin{gathered} r=0.07\times100 \\ r=7 \end{gathered}$

The growth rate is 7%.