Answer:
After 2.9 years the town's tax status will change
The towns tax status change within the next 3 years
Step-by-step explanation:
The question below is
Will the towns tax status change within the next 3 years ?
Let
y -----> the population of a small town
t ----> the number of years
we have a exponential function of the form
where
a is the initial value
b is the base
In this problem
substitute
Remember that
The town's tax status will change once the population is below 6,000 people
so
The inequality that represent this situation is
Solve for t
Apply log both sides
Multiply by -1 both sides
so
After 2.9 years the town's tax status will change
therefore
The answer is
Yes, the towns tax status change within the next 3 years