Question

Cesium chloride is a radioactive substance that is sometimes used in cancer treatments. Cesium chloride has a biological half-life of 4 months. (Note: Use the concepts of half-life or doubling time. The biological half-life of a substance is the amount of time it takes for the physiologic or radiologic activity of that substance to reduce by half.)
Required:
a. Find a model for the amount of cesium chloride left in the body x months after 840 mg has been injected.
b. How long will it take for the level of cesium chloride to fall below 3%?

Answer 1

Step-by-step explanation:

my workings and answers is in the image above

Answer 2

Answer:

There is another approach to this problem that

might be more in line with what you are studying ..... NOTE: the first answer is correct.

Step-by-step explanation:

1 = 2$x^{4}$

1/2 = $x^{4}$

ln(1/2) = 4 ln(x)

ln(1/2)/4 = ln(x)

x = $e^{-0.1732}$

x = .8408

~~~~~~~~~~~~~~~~

model : 840$(0.8408)^{t}$

~~~~~~~~~~~~~~~~~

(.03* 840)  = 840$(0.8408)^{t}$

(.25.2)  = 840$(0.8408)^{t}$

.03 = $(0.8408)^{t}$

ln(.03 )=ln( $(0.8408)^{t}$)

t = ln(.03 )/ln(0.8408 )

t = 20.22