In an Idealized Experiment, the Following Results Were Obtained for a Population

question 146

Essay

In an idealized experiment, the following results were obtained for a population of bacteria during a 7 hour period. The initial population is 1000 bacteria. $$\begin{array} { | | l | c | c | c | c | c | c | c | | } \hline \hline \text { Time (hours) } & 0.5 & 1.0 & 1.5 & 2.0 & 2.5 & 3.0 & 3.5 \\\hline \text { Number of Bacteria } & 10 ^ { 3 } & 10 ^ { 3 } & 3.2 \times 10 ^ { 3 } & 10 ^ { 4 } & 3.2 \times 10 ^ { 4 } & 10 ^ { 5 } & 3.2 \times 10 ^ { 5 } \\\hline \hline \text { Time (hours) } & 4.0 & 4.5 & 5.0 & 5.5 & 6.0 & 6.5 & 7.0 \\\hline \text { Number of Bacteria } & 10 ^ { 6 } & 3.2 \times 10 ^ { 6 } & 10 ^ { 7 } & 3.2 \times 10 ^ { 7 } & 10 ^ { 8 } & 3.2 \times 10 ^ { 8 } & 10 ^ { 9 } \\\hline \hline\end{array}$$ (a) Identify the period where there is no change in the number of bacteria. (This is called the period of adaptation.)
(b) Identify the period of growth.(c) Assume that the growth rate of bacteria is proportional to the population. Find an exponential model for the data during the period of growth.(d) Add an additional line to the table using your population model to generate the entries for the given time values. Compare these entries with the given data and explain any discrepancy.

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