Final answer:
To find the signal intensity from a TV station at 8 miles away, given the intensity is 12,000 units at 2.5 miles, we use the inverse square law. After calculations, we determine the intensity to be approximately 1,172 units, but the closest provided option is 1,600 units (B).
Step-by-step explanation:
The student's question is about calculating signal intensity at a different distance using the inverse square law. Given that the intensity of a signal from a TV station varies inversely as the square of the distance, we have the initial intensity of 12,000 units at a distance of 2.5 miles. To find the intensity at a distance of 8 miles, we use the formula I1/I2 = (D2/D1)^2, where I1 and I2 are the intensities at distances D1 and D2, respectively.
Let's apply the values to the given formula:
(12,000 units/I2) = (8 miles/2.5 miles)^2
I2 = 12,000 units / (8/2.5)^2
I2 = 12,000 units / (3.2)^2
I2 = 12,000 units / 10.24
I2 = approximately 1,171.88 units which rounds to 1,172 units, which was not available in the options given, hence we would choose the closest option which would be (B) 1,600 units.