Question

Light is absorbed when it passes through a glass window. If r% of light is absorbed by a glass with thickness w , then the percent of light that is absorbed by a piece of glass with a thickness nw of for any natural number n is modeled by the following function:

A(n) = 100 [1 - (1 - r/100)^n], f or 0 _< r _< 100

a. Show that is an increasing function of n if 0 < r < 100.

b. Sketch the graph of A when r = 10.

c. Evaluate limn oo A(n) and interpret the results.

No one has answered this question yet.

Answer 1

v=1-r/100 <1, so it's a fraction
as n increases, z=v^n thus decreases

so, 100[1-z] increases

use your favorite graphing calculator or online grapher to sketch thebgraph

As n gets large, A(n) approaches 100, since z approaches zero.

Answer 2

Hello Steve. Thank you for your help. Can you please explain the steps and in details, so i will know where my problem was. Once again thanks.