Q. 101 - Precalculus Enhanced with Graphing Utilities

Question

 Optics If a single pane of glass obliterates $3\%$ of the light passing through it, the percent p of light that passes through n successive panes is given approximately by the function 

  $p\left(n\right)=100{(0.97)}^n$

(a) What percent of light will pass through 10 panes?
(b) What percent of light will pass through 25 panes? 

Step-by-Step Solution

Answer

(a) $73.74\%$

(b) $46.69\%$

Step 1.Giveninformation

Let us consider a pane which blocks $3\%$ of the light.
This means that the light passing through the pane is $97\%$ of the actual.
Thus the percentage of light that passes through n panes 

$p\left(n\right)=100{(0.97)}^n$

Step 2.(a) What percent of light will pass through 10 panes?

Let us consider 10 panes.
Therefore light passing through 10 panes will be

$$\begin{gathered} p\left(10\right)=100{(0.97)}^{10} \\ =100(0.7374) \\ =73.74\% \end{gathered}$$

Step 3. (b) What percent of light will pass through 25 panes?

Let us consider 25 panes
Therefore light passing through 25 panes will be 

$$\begin{gathered} p\left(25\right)=100{(0.97)}^{25} \\ =100(0.4669) \\ =46.69\% \end{gathered}$$