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

There is another approach to this problem that

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

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

Answer 2

Explanation:

my workings and answers is in the image above