A biochemical reaction in which a substance S is both produced and consumed is investigated. The concentration c(t) of S changes during the reaction, and is seen to follow the differential equation
. . . . .\(\displaystyle \dfrac{dc}{dt}\, =\, K_{max}\, \dfrac{c}{k\, +\, c}\, -\, rc\)
where Kmax, k, r are positive constants with certain convenient units. The first term is a concentration-dependent production term and the second term represents consumption of the substance.
(a) What is the maximal rate at which the substance is produced? At what concentration is the production rate 50% of this maximal value?
(b) If the production is turned off, the substance will decay. How long would it take for the concentration to drop by 50%?
(c) At what concentration does the production rate just balance the consumption rate?
Can someone show me how to do question A?
. . . . .\(\displaystyle \dfrac{dc}{dt}\, =\, K_{max}\, \dfrac{c}{k\, +\, c}\, -\, rc\)
where Kmax, k, r are positive constants with certain convenient units. The first term is a concentration-dependent production term and the second term represents consumption of the substance.
(a) What is the maximal rate at which the substance is produced? At what concentration is the production rate 50% of this maximal value?
(b) If the production is turned off, the substance will decay. How long would it take for the concentration to drop by 50%?
(c) At what concentration does the production rate just balance the consumption rate?
Can someone show me how to do question A?
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