An object is moving away from the light source at a rate of 4 units/s. Find the rate of change of the intensity of illumination when it is 2 units from the light source.
yeah, this is my answer:
rate of change = k(1/unit˛xsecond)
The intesity of illumination as a function of distance $\displaystyle r$ from a point source is:Originally Posted by mathletes
$\displaystyle I(r)=I(1)/r^2$,
where $\displaystyle I(1)$ is the intensity of illumination at a distance of $\displaystyle 1$ unit from the source.
Now:
$\displaystyle \frac{d}{dt} I(r)=I(1)\frac{-2}{r^3}\ \frac{dr}{dt}$.
So now you only need to plug in $\displaystyle r=2$ and $\displaystyle \frac{dr}{dt}=4$ to get the answer, in units of
(whatever you are using as units of intensity)/s.
RonL