Yeast is used in bread baking; it has a rapid doubling time of approximately 90 minutes. (note: use the concepts of half-life or doubling time.) (a) find a model for the size of a yeast culture after t hours, given the original size was 1.5 teaspoons. (round all numerical values to three decimal places.)

Yeast Yeast is used in bread baking; it has a rapid doubling time of approximately 90 minutes. a. Find a model for the size of a yeast culture after t hours, given the original size was 2.5 teaspoons.

Explanation:

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tatendagota tatendagota · Answer 2 · 2020-03-08T01:57:40+01:00

Answer:

[tex]N = 90N_{0} + C[/tex]

Explanation:

Thinking process:

Let the number of yeast species be N

the rate of doubling be given by the expression: [tex]\frac{dN}{dt}[/tex]

The doubling time = 90 mins

Thus, the rate equation will be: [tex]\frac{dN}{dt} = KN[/tex]

Rearranging gives:

[tex]dN = KNdt[/tex]

Integrating the two sides gives:

[tex]\int\limits^a_b {dN} \, = \int\limits^a_b {KN} \, dt[/tex]

N = KNt + C

or

[tex]N= N_{0} t + C[/tex]

this is the number of yeast at the time t

at t = 0, there are 1.5, and N = C

after t = 90 mins, the number of teaspoons will be:

N = [tex]90N_{0} + C[/tex]