As a town gets smaller, the population of its high school decreases by 6% each year, the senior class has 160 students now. in how many years will it have about 100 students. write an equation. then solve the equation without graphing

For this case we have an equation of the form:
 y = A * (b) ^ t
 Where,
 A: initial amount
 b: decrease rate
 t: time in years
 Substituting values we have:
 y = 160 * (0.94) ^ t
 For 100 students we have:
 160 * (0.94) ^ t = 100
 Clearing t we have:
 (0.94) ^ t = 100/160
 log0.94 ((0.94) ^ t) = log0.94 (100/160)
 t = log0.94 (100/160)
 t = 7.6 years
 
 it will have about 100 students in:
 t = 7.6 years

The answer is $9.90 with rounding to the nearest tenth