The intensity I of light form a light bulb varies inversely as the square of the distance d from the light bulb. Suppose I is 490 w/m2 when the distance is 4 m. How much farther would it be to a point where the intensity is 250 w/m2?
First, familiarize yourself with the problem. You told that the intensity, I of light from the light bulb varies inversely as the square of the distance d to the light bulb.
This means the intensity and distance can be related by the equation
Solve to get k = 7840.
Substitute into the formula for intensity,
Next , transfer the problem. You want to find how much farther away you would to be for the intensity to be 250 w/m2. If the additional distance is x, write an equation that relates this distance to the intensity of 250 w/m2.
The distance d = 4 +x.
Thus, the equation can be written to relate this distance to the intensity.
To simplify, multiply through by a common denominator.
250*(4+x)2 = 7840
Divide both sides by 250 to isolate the quadratic square.
Take the square root of both sides. Since 4+x is supposed to represent a distance, only the positive square root needs to be considered.
4 + x =
4 + x =
Solve this for x by subtracting 4 from both sides.
x = -4
Always check your answer. Substitute x = and find that the intensity is equal to 250 w/m, just as expected.
Finally, convert the fraction to a decimal. You would have to be an additional 1.6 meter(s) away to reduce the intensity to 250 w/m2.