Variable Amount of Compound

[mathdad]

A self-catalytic chemical reaction results in the formation of a compound that causes the formation ratio to increase. If the reaction rate V is modeled by
V(x) = kx(a - x), given 0 is less than or equal to x less than or equal to a, where k is the positive constant, a is the initial amount of the compound, and x is the variable amount of the compound, for what value of x is the reaction rate a maximum?

Solution:

V(x) = kx(a - x)

V(x) = kax - kx^2

I will now use x = -b/2a.

x = -(ka)/2(-k)

x = ka/2k

x = a/2

Correct?

 

[Otis]

Yes, it looks good.

Here are two notes about typed notation.

... V(x) = kax - kx^2

I will now use x = -B/(2A).
x = -ka/(-2k)
x = ka/(2k) ...

Above, I put grouping symbols around the denominators, and I changed coefficient symbols a and b to A and B because symbol a is already in use (initial amount of compound).

?

 

[mathdad]

Yes, it looks good.

Here are two notes about typed notation.


Above, I put grouping symbols around the denominators, and I changed coefficient symbols a and b to A and B because symbol a is already in use (initial amount of compound).

?

Ok. Works for me. Thanks.