Question

The intensity, io, of a light source is reduced to i after passing through d meters of fog according to the formula i = ioe−0.22d. if 3,000 lumens of light are present initially, what is an equivalent expression written as a percentage rate of lumens lost? hint: find the value of e−0.22 on your calculator.

Answer 1

For this case, the first thing we should do is rewrite the expression.
 We have then:
 i = io * e ^ (- 0.22 * d)
 Rewriting:
 i = io * (e ^ (- 0.22)) ^ d
 i = 3000 * (e ^ (- 0.22)) ^ d
 i = 3000 * (0.802518798) ^ d
 Answer:
 an equivalent expression written as a percentage rate of lumens lost is:
 i = 3000 * (0.802518798) ^ d