Question

13 mark for review
$f(t)=500(0.5)^{\frac{1}{12}}$ 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?
a 500
b 12
c 5
d 2

Explanation:

Step1: Identify the value of t

At the surface of the sample of iron, $t = 0$.

Step2: Substitute t into the function

Substitute $t = 0$ into $f(t)=500(0.5)^{\frac{t}{12}}$. We get $f(0)=500(0.5)^{\frac{0}{12}}$.
Since any non - zero number to the power of 0 is 1, $(0.5)^0 = 1$. So $f(0)=500\times1 = 500$.

Answer:

A. 500