Rates/ratios problem

Thanks.

How did it get smaller? How does this get smaller: y = k/sqrt(x). So this is how I am suppose to solve inverse problems? Doing/using this formula/work?

Yes you use this fact

Let k be a constant that you will often need to find using information from the question.

 

If y is directly proportional to x then    

 

$y=kx$

 

If you graph x agains y you will get a straight line.  

The y interept is 0

aand the gradient is k

 

OR

 

If y is inversely proportional to x then 

 

$y=\frac{k}{x}$

 

This time if you graph it it will be a hyperbola. 

If k is positive it will be in the first and 3rd quad

and if k is neg it will be in the 2nd and 4th quads.

 

Now consider the case there k is +1

If x=2    y=1/2

If x=4     y=1/4

See, as x gets bigger, y gets smaller.   (that is when k is positive)

In your question, y varies inversly to sqrtx

so you must start with:

 

$y=\frac{k}{\sqrt{x}}$

 

then sub in (2,4) to determine the value of k

 

Once you have k then you have a formula that you can use for determining the y value of any x value.