Q. 104 - Precalculus Enhanced with Graphing Utilities

Question

 Healing of Wounds The normal healing of wounds can be modeled by an exponential function. If A₀ represents the original area of the wound and if  equals the area of the wound, then the function

$A\left(n\right)=A_0{e}^{-0.35n}$

describes the area of a wound after n days following an injury when no infection is present to retard the healing. Suppose that a wound initially had an area of 100 square millimeters.
(a)   If healing is taking place, how large will the area of the wound be after 3 days?
(b)   How large will it be after 10 days? 

Step-by-Step Solution

Answer

(a)  $34.99mm$

(b)  $3.01mm$

Step 1.Given information

Let us consider the area of the wound be A₀.
And the area of the wound after n days be 

$A\left(n\right)=A_0{e}^{-0.35n}$

Step 2.(a) If healing is taking place, how large will the area of the wound be after 3 days?

 Let us consider A₀ be $100mm$ and after 3 days new area will be

$$\begin{gathered} A\left(n\right)=A_0{e}^{-0.35n} \\ A\left(3\right)=100e^{-0.35\times 3} \\ =34.99mm \end{gathered}$$

Step 3.(b) How large will it be after 10 days?

Let us consider A₀ be $100mm$ and after 10 days new area will be

$$\begin{gathered} A\left(n\right)=A_0{e}^{-0.35n} \\ A\left(10\right)=100e^{-0.35\times 10} \\ =3.01mm \end{gathered}$$