Answer:
(a)96.77%
(b)3.23%
Step-by-step explanation:
Starting with the Michaelis-Menten equation which is used to model biochemical reactions:
Dividing both sides by [tex]V_{\max }}[/tex]
[tex]\dfrac{v}{V_{max}}=\dfrac{[S]}{K_M + [S]}[/tex]
Where: [tex]V_{\max }} =[/tex] maximum rate achieved by the system
[tex]K_{\mathrm {M} }}[/tex]=The Michaelis constant
[tex]{\displaystyle {\ce {[S]}}}=[/tex] Substrate concentration
(a) When [tex][S]=30K_M[/tex]
[tex]\dfrac{v}{V_{max}}=\dfrac{[S]}{K_M + [S]}\\\dfrac{v}{V_{max}}=\dfrac{30K_M}{K_M + 30K_M}\\\dfrac{v}{V_{max}}=\dfrac{30}{1 + 30}\\\dfrac{v}{V_{max}}=\dfrac{30}{31}\\$Expressed as a percentage\\\dfrac{v}{V_{max}}=\dfrac{30}{31}X100=96.77\%[/tex]
(b)When [tex]K_M=30[S][/tex]
[tex]\dfrac{v}{V_{max}}=\dfrac{[S]}{K_M + [S]}\\\dfrac{v}{V_{max}}=\dfrac{[S]}{30[S] + [S]}\\\\=\dfrac{1[S]}{30[S] + 1[S]}\\=\dfrac{1}{30 + 1}\\\dfrac{v}{V_{max}}=\dfrac{1}{31}\\$Expressed as a percentage\\\dfrac{v}{V_{max}}=\dfrac{1}{31}X100=3.23\%[/tex]
