Answer to Question #159143 in Algebra for Jan

Question

Gels used to change the colour of spotlights each reduce the intensity of the light by 4%. The algebraic model for this situation is

I 5 100(0.96)n.

a) Describe what each part of the equation represents.

b) Determine the intensity of the spotlight if three gels are used.

c) How many gels would reduce the intensity by more than 75%?

Answer 1

given that intensity decreases with using the gels as $I=100(.96)^n$

this equation can be written as $I=100(1-\frac{R}{100})^n$

a)

initially assume intensity of spotlight is 100%.

I = intensity of spotlights

R = rate of reduced intensity in percentage.

n = no. of gels used

b)

if 3 gels are used

$I=100(1-\frac{4}{100})^3=100(.96)^3=88.47$

c)

let the intensity is 25% then

$25=100(.96)^n$

$.25=(.96)^n$

$n\approxeq34$

thus, 34 gels are used to decreases the intensity of spotlight more than 75%.