Answer:
The answer is below
Step-by-step explanation:
An exponential decrease can be represented by the formula:
[tex]y=ab^x[/tex]
where a is the initial amount and b < 1.
Let p represent the population after t years, hence:
[tex]p=ab^t[/tex]
Since the population decreases exponentially at a rate of 14.3% each year, hence:
b = 100% - 14.3% = 85.7% = 0.857
b = 0.857
Also, a = 9400 people
Therefore the equation is:
[tex]p=9400(0.857^t)\\[/tex]
The town's tax status will change once the population is below 6,000 people, therefore:
[tex]9400(0.857^t)<6000\\[/tex] for the tax status to change.
At t = 3 years:
[tex]p=9400(0.857^3)=5917\\\\5917<6000,hence\ the\ towns\ tax\ status\ would \ change\ after\ 3\ years\\[/tex]
