Question 394562
Let w = # weeks 
Then after w weeks , the price becomes {{{500*0.75^w}}}.
Then we want {{{100 < 500*(0.75)^w}}}, or {{{0.20 < 0.75^w}}}.
If w = 5, {{{0.75^5 = 0.2373}}} to four decimal places.
If w = 6, {{{0.75^6 = 0.187}}} to 3 decimal places.
So AFTER 6 weeks, the price should be less than $100. 

Though technically speaking  it will only take {{{ln0.2/ln0.75 = 5.59}}} weeks (or after 5 weeks and Thursday of the new week) for the price to be lower than $100.