Question

the population of a small town is decreasing exponentially at a rate of 14.3% each year. The current population is 9,400 people. The town's tax status will change once the population is below 6,000 people. create an inequality that can be used to determine after how many years,t, the towns taxes status will change.

Answer 1

For this case, we have a function of the form:

`y = A * (b) ^ t`
Where,
A: initial amount
b: decrease rate
t: time in years
Then you have the following inequality:

`9400 * (0,857) ^ t \ \textless \ 6000`
Answer:
An inequality that can be used to determine after how many years, t, will change the tax status of cities is:

`9400 * (0,857) ^ t \ \textless \ 6000`