Answer
$P=250 W/m^2$
Work Step by Step
A formula relating the power, intensity, and distance from a source is $$I=\frac{P}{A}=\frac{P}{4\pi r^2}$$ This means that if $\frac{1}{r^2}$ is separated to express the formula as $$I=(\frac{P}{4\pi})(\frac{1}{r^2})$$ a linear regression can be formed with $I$ as the y-axis, $\frac{1}{r^2}$ as the x-axis, and $\frac{P}{4\pi}$ as the slope. To find the slope, use the formula $$m=\frac{\Delta y}{\Delta x}$$ Since two units on the x-axis is $x=8.0 m^{-2}$, two and a half units would be $x=10. m^{-2}$. $I_s$ is equal to $200 W/m^2$. This allows for a slope measurement of $$m=\frac{200 W/m^2}{10.m^{-2}}=20. W/m^2$$ Finally, by using the relation that $m=\frac{P}{4\pi}$ allows one to solve for $P$ and substitute known values to get a power value of $$P=4\pi m = 4\pi (20W)=250 W/m^2$$
