Question

Technetium-99m is a drug taken by a patient and then used to study tumors in the brain, lungs andother parts of the body. A patient takes a 1000-mg pill. The data below shows how much activeIngredient remain in the body over 6 hour time intervals

Answer 1

Given the function:

A) Initial value.

The initial value is the amount of drug at the time interval of zero.

Thus,

`\begin{gathered} initial\text{ value }\Rightarrow amount\text{ of drug at t=o} \\ =1000\text{ mg} \end{gathered}`

Thus, the initial value is 1000.

B) Decay rate factor.

From the decay rate formula expressed as

`\begin{gathered} y=a(b)^t \\ where \\ a\Rightarrow initail\text{ amount} \\ b\Rightarrow decay\text{ factor} \\ t\Rightarrow time \end{gathered}`

From the table,

`\begin{gathered} when\text{ t=1, y=500} \\ substituting\text{ these values into the decay rate formula, we have} \\ 500=a(b)^1 \\ where\text{ a =1000} \\ \Rightarrow500=1000(b) \\ divide\text{ both sides by 1000,} \\ (500)/(1000)=b \\ \Rightarrow0.5=b \\ \end{gathered}`

Thus, the decay factor is

`0.5`

C) Rule for the function.

Thus, substituting the values of 1000 and 0.5 for a and r into the decay rate formula, we have the rule of the function to be expressed as

`\begin{gathered} y=a(b)^t \\ \Rightarrow A(t)=1000(0.5)^t \end{gathered}`