SOLUTION: The intensity, L1, of light transmitted through a certain type of tinted glass, t, mm thick can be found with the formula {{{L1(t)= L0(10)^(-.034t)}}} , where L0 is the intensity b

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: The intensity, L1, of light transmitted through a certain type of tinted glass, t, mm thick can be found with the formula {{{L1(t)= L0(10)^(-.034t)}}} , where L0 is the intensity b      Log On


   



Question 867341: The intensity, L1, of light transmitted through a certain type of tinted glass, t, mm thick can be found with the formula L1%28t%29=+L0%2810%29%5E%28-.034t%29 , where L0 is the intensity before entering the glass. How thick should the glass be in order to block 30% of the light?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If you block 30% of the light, then the light intensity after it passes through the glass will be 100 - 30 = 70%. Therefore, L1(t) = 0.7*L0 (basically 70% of the original light intensity L0 coming in). Plug this is in and solve for t


L1%28t%29=+L0%2810%29%5E%28-.034t%29


0.7%2AL0=+L0%2810%29%5E%28-.034t%29


0.7%2AL0%2FL0+=+%28L0%2810%29%5E%28-.034t%29%29%2FL0


0.7+=+%2810%29%5E%28-.034t%29


ln%280.7%29+=+ln%28%2810%29%5E%28-.034t%29%29


ln%280.7%29+=+-0.034t%2Aln%2810%29


ln%280.7%29+=+-0.034%2Aln%2810%29%2At


ln%280.7%29%2F%28-0.034%2Aln%2810%29%29+=+t


4.55593999958068+=+t


t+=+4.55593999958068 This is the approximate thickness.