Question

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

Answer 1

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
Answer:
it will have about 100 students in:
t = 7.6 years