Question

Biochemists studying enzyme kinetics encounter formulas of the form fox)-(K/Vx+1/V. where K and V are constants. Use this information to answer parts (a) and (b). (a) If fx) 0.2x+8, find K and V so that fx) may be written in the form fix) (K/V)x+ 1/V (b) Find the x-intercept and y-intercept of the line y (K/V)x+1/V (n terms of K and V). (a) K (Simplify your answer. Type an integer or a fraction.)

Answer 1

a) V=0.125 and K=0.025

b) Y-intercept = 1/V and X-intercept = -1/K

Explanation:

a)

If

`\bf f(x)=(K)/(V)x+(1)/(V)`

and also

f(x) = 0.2x + 8

Then

`\bf (1)/(V)=8\rightarrow V=(1)/(8)`

`\bf \boxed{V=0.125}`

`\bf (K)/(V)=(K)/(0.125)=0.2\rightarrow\boxed{K=0.025}`

b)

The Y-intercept is gotten when x=0, so the Y-intercept is
`\bf \boxed{(1)/(V)}`

The X-intercept is gotten when y=0 (f(x)=0) so

`\bf 0=(K)/(V)x+(1)/(V)\rightarrow(K)/(V)x=-(1)/(V)\rightarrow x=-(1)/(K)`

and the X-intercept is

`\bf \boxed{x=-(1)/(K)}`

K and V written as fractions are

`\bf K=(25)/(1000)=(1)/(40)`

`\bf V=(1)/(8)`