Respuesta :
Answer:
The initial population at the beginning of the 10 years was 129.
Step-by-step explanation:
The population of the village may be modeled by the following function.
[tex]P(t) = P_{0}e^{rt}[/tex]
In which P is the population after t hours, [tex]P_{0}[/tex] is the initial population and r is the growth rate, in decimal.
In this problem, we have that:
[tex]P(10) = 158, r = 0.02[/tex].
So
[tex]158 = P_{0}e^{0.02*10}[/tex]
[tex]P_{0} = 158*e^{-0.2}[/tex]
[tex]P_{0} = 129[/tex]
The initial population at the beginning of the 10 years was 129.
Answer:
Step-by-step explanation:
The formula representing the population growth after t years can be expressed as
A = P(1+r/n)^nt
Where
A is the population of the village after t years.
P represents the initial population of the village at the beginning of the 10 years.
r represents population growth rate
n represents the number of times that the population was compounded in each year.
From the given information,
A = 158
r = 2% = 2/100 = 0.02
t = 10 years
n = 1 because it was compounded continuously each year.
Therefore
158 = P(1+0.02/1)^1×10
158 = P(1.02)^10
P = 158/(1.02)^10 = 129.615
Approximately 130 to the nearest whole number.
