# The shutter speed, S, of a camera varies inversely as the square of the aperture setting, f. When f=8, S=125. How do you find a formula for S in terms of f?

Apr 25, 2017

I got: $S \left(f\right) = \frac{8000}{f} ^ 2$

#### Explanation:

We can try using:
$S \left(f\right) = \frac{A}{f} ^ 2$
where $A$ is a constant that we need to find.

We use the fact that when $f = 8$ then $S = 125$ in the above formula:

$125 = \frac{A}{8} ^ 2$

rearranging:

$A = 125 \cdot {8}^{2} = 8000$

So our function is:

$S \left(f\right) = \frac{8000}{f} ^ 2$