I'm doing an exercise in calculus about functions as math models, and I'm stuck in this one particular exercise about representing a pendulum's period. The problem goes:

The period of a pendulum is directly proportional to the square root of the length of the pendulum, and a pendulum of length 8 feet has a period of 2 seconds.

So, by definition of "directly proportional to the square root of the length of the pendulum", we have:

$$f(x) = k \sqrt x$$

This next part is where I'm not sure; "a pendulum of length 8 feet has a period of 2 seconds.":

$$2= 8k$$

hence

$$k = 1/4$$

Plugging that in, I arrived with:

$$f(x) = \frac {\sqrt {x} }{4} $$

I took a look at the math model answer and the book says that the correct mathematical model is 

$$f(x) = \sqrt \frac{x}{2} $$

and that if you were to find the period of a pendulum with length 2 feet, it is 1 second.