Respuesta :
Answer:
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:
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]