In 2018, the population of West Littleton was 5,100. The following year, the population was 4,998.
Let t represent the number of years since 2018. Assuming the population continues to decrease exponentially, which expression best models the population of West Littleton over time?
According to this model, what will the population be in 2027?
Round your answer to the nearest whole number.
people
The exponential decay model for the population of West Littleton would be:
Population = 5,100 * (1 - r)^t
where r is the rate of decrease and t is the number of years since 2018.
Since the population decreased from 5,100 to 4,998 in one year, we can plug in the values to find the rate of decrease:
4,998 = 5,100 * (1 - r)^1
(1 - r) = 4,998 / 5,100
(1 - r) = 0.98039215686
r = 1 - 0.98039215686
r = 0.01960784313
So, our exponential decay model for the population of West Littleton is:
Population = 5,100 * (1 - 0.01960784313)^t
To find the population in 2027 (9 years after 2018), we substitute t = 9 into the equation:
Population = 5,100 * (1 - 0.01960784313)^9
Population ≈ 5,100 * (0.98039215686)^9
Population ≈ 5,100 * 0.9162497
Population ≈ 4,665
Therefore, the population of West Littleton in 2027, according to the exponential decay model, will be approximately 4,665 people.