f t = 500 0.5 t 12 The function f models the intensity of an X-ray beam, in number of

Question

f t = 500 0.5 t 12 The function f models the intensity of an X-ray beam, in number of particles in the X-ray beam, t millimeters below the surface of a sample of iron. According to the model, what is the estimated number of particles in the X-ray beam when it is at the surface of the sample of iron?

Accepted Answer

Choice A is correct. It's given that the function f models the intensity of an X-ray beam, in number of particles in the X-ray beam, t millimeters below the surface of a sample of iron. When the X-ray beam is at the surface of the sample of iron, it is 0 millimeters below the surface, so the value of t is 0 . Substituting 0 for t in the function f t = 500 0.5 t 12 yields f 0 = 500 0.5 0 12 . Since any positive number raised to the power of 0 is equal to 1 , it follows that f 0 = 500 1 , or f 0 = 500 . Therefore, the estimated number of particles in the X-ray beam at the surface of the sample of iron is 500 . Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

Question 044c08