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 of nw for any natural number n is modeled by the following function : A (n ) = 100 [1 - (1 - r/100) ^n ] , for 0

Question

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 of nw for any natural number n is modeled by the following function : A (n ) = 100 [1 - (1 - r/100) ^n ] , for 0 <,= r <= 100 a. Sketch the graph of A when r = 10. b. Evaluate lim n approaches to infinity A (n ) and interpret the results.

Steve · Answer

well, since (1-r/100) < 1, the limit is zero as n->∞. So, as you'd expect, lim(A) = 100% visit wolframalpha and enter 100 [1 - (1 - 10/100) ^n ] for the plot.

Scottie · Answer

Thanks Steve