Respuesta :
Answer:
The population of the town of 2020 is approximately 6847
Step-by-step explanation:
The given population of the small town is 2002, P₀ = 10,800
The annual percentage decrease in the population, r = 2.5%
The date at which the new population,'P', is required = 2020
Therefore;
The number of years over which the population changes, 't', is given as follows;
t = 2020 - 2002 = 18
The number of years over which the population changes, t = 18 years
Given that the population is decreasing, we get;
The general formula for exponential decay is given as follows;
[tex]P = P_0 \cdot (1 - r)^t[/tex]
Therefore, the population, 'P', of the town of 2020 which is in t = 18 years, is given as follows;
[tex]P = 10,800 \times(1 - 0.025)^{18} = 6847.10263915[/tex]
Given that the population is given in whole numbers, we round down to the nearest whole number population of people as follows;
The population of the town of 2020, P ≈ 6847.
