Answer
$(a)$ $I=\frac{k}{d^2}$
$(b)$ $k=64000$
$(c)$ $I=160$
Work Step by Step
$(a)$ According to the information given, we can write the following relation:
$I=\frac{k}{d^2}$
$(b)$ To find the constant of proportionality, we have to use the information given.
If $I=1000$ and $d=8m$
$1000=\frac{k}{8^2}$
$k=1000\times 64$
$k=64000$
$(c)$ If $d=20m$
$I=\frac{64000}{20^2}=\frac{64000}{400}=160$
$I=160$
