Question

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(n)=100(0.97)^n. (a) what percent of light will pass through 5 panes? (round to the nearest whole number as needed.) (a) the percent of light that will pass through 15 panes is approximately ___%. (round to the nearest whole number as needed.) (c) choose the correct answer below. a. each pane allows only 97% of light to pass through. b. each pane allows only 3% of light to pass through. c. each pane allows only 0.03% of light to pass through. d. each pane allows only 0.97% of light to pass through.

Explanation:

Step1: Calculate light - passing percentage for 5 panes

The formula for the percentage of light passing through $n$ panes is $p(n)=100(0.97)^n$. For $n = 5$, we have $p(5)=100\times(0.97)^5$.
$p(5)=100\times0.8587340257 = 85.87340257\approx86\%$.

Step2: Calculate light - passing percentage for 15 panes

For $n = 15$, we use the formula $p(15)=100\times(0.97)^{15}$.
$(0.97)^{15}=0.6332485734$, so $p(15)=100\times0.6332485734 = 63.32485734\approx63\%$.

Step3: Analyze the meaning of the base 0.97

The base 0.97 represents the proportion of light that passes through a single pane of glass. Since the glass obliterates 3% of the light passing through it, the proportion of light that passes is $1 - 0.03=0.97$.

Answer:

(a) 86%
(b) 63%
(c) The base 0.97 represents the proportion of light that passes through a single pane of glass. Since 3% of the light is obliterated by a single pane, the proportion of light that passes is 97% or 0.97 in decimal form.
A. Each pane allows only 97% of light to pass through.