$\"\"$

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(a)

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Plot the data:

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$\"\"$

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Observe the graph:

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The graph converges to $\"\"$ .

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The carrying capacity of the yeast population is $\"\"$ .

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$\"\"$

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(b)

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Relative growth rate is $\"\"$ , $\"\"$ is a constant.

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Initial relative growth rate is $\"\"$ , where $\"\"$ is initial value of $\"\"$ , $\"\"$ is change in $\"\"$ and $\"\"$ is change in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The initial relative growth rate is $\"\"$ .

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$\"\"$

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(c)

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The exponential model is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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The exponential model is $\"\"$ .

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The logistic model equation is $\"\"$ , where $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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The logistic model is $\"\"$ .

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$\"\"$

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(d)

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Construct a table:

\

Predict the values from exponential model and logistic model:

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Time in hours	Observed values	Exponential model	Logistic model
\ $\"\"$ \	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$

\

\

Compare the observed values with predict values of exponential model and logistic model.

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Observe that logistic model is fits in better as compared to the exponential model.

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Graph:

\

Plot the given data.

\

Graph the exponential equation $\"\"$ and logistic equation $\"\"$ .

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$\"\"$

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Observe the graph:

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The logistic model is fits in better as compared to the exponential model.

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$\"\"$

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(e)

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The logistic model is $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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In logistic model the number of yeast cells after $\"\"$ is $\"\"$ yeast cells.

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$\"\"$

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(a)

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Graph:

\

$\"\"$

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The carrying capacity of the yeast population is $\"\"$ .

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(b) The initial relative growth rate is $\"\"$ .

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(c) The exponential model is $\"\"$ .

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The logistic model is $\"\"$ .

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(d) The logistic model is fits in better as compared to the exponential model.

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(e) In logistic model the number of yeast cells after $\"\"$ is $\"\"$ yeast cells.