$\"\"$

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(a)

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

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At time $\"\"$ , the culture weighs $\"\"$ .

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At time $\"\"$ , the culture weighs $\"\"$ .

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The maximum weight of the culture is $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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

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$\"\"$ .

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Substitute $\"\"$ and $\"\"$ 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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$\"\"$

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$\"\"$

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$\"\"$ .

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

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$\"\"$ .

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$\"\"$

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(b) Find the culture weight after $\"\"$ .

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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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After $\"\"$ the weight of the culture is $\"\"$ .

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$\"\"$

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(c) When will the culture weight reaches $\"\"$ .

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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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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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(d)

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The differential equation is in the form of logistic differential equation $\"\"$ .

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

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The differential equation is $\"\"$ .

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The initial condition is $\"\"$ .

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Step size is $\"\"$ .

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Euler $\"\"$ s Method :

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Using $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

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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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The culture weight is $\"\"$ .

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$\"\"$ is increasing most rapidly where $\"\"$ , corresponds to $\"\"$ .

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$\"\"$

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(a) $\"\"$ .

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(b) After $\"\"$ the weight of the culture is $\"\"$ .

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(c) $\"\"$ .

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(d) $\"\"$ ; $\"\"$ .

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(e) $\"\"$ .