Respuesta :
Given Information:
Starting population = P₀ = 45
rate of growth = 22%
Required Information:
Population every five years from this year to the year 2050 = ?
Answer:
[tex]Year \: 2020 = P(0) = 45e^{0} = 45\\\\Year \: 2025 = P(5) = 45e^{0.22*5} = 135\\\\Year \: 2030 = P(10) = 45e^{0.22*10} = 406\\\\Year \: 2035 = P(15) = 45e^{0.22*15} = 1,220\\\\Year \: 2040 = P(20) = 45e^{0.22*20} = 3,665\\\\Year \: 2045 = P(25) = 45e^{0.22*25} = 11,011\\\\Year \: 2050 = P(30) = 45e^{0.22*30} = 33,079\\\\[/tex]
Step-by-step explanation:
The population growth can be modeled as an exponential function,
[tex]P(t) = P_0e^{rt}[/tex]
Where P₀ is the starting population, r is the rate of growth of the population and t is the time in years.
We are given that starting population of 45 and growth rate of 22%
[tex]P(t) = 45e^{0.22t}[/tex]
Assuming that the starting year is 2020,
[tex]Year \: 2020 = P(0) = 45e^{0} = 45\\\\Year \: 2025 = P(5) = 45e^{0.22*5} = 135\\\\Year \: 2030 = P(10) = 45e^{0.22*10} = 406\\\\Year \: 2035 = P(15) = 45e^{0.22*15} = 1,220\\\\Year \: 2040 = P(20) = 45e^{0.22*20} = 3,665\\\\Year \: 2045 = P(25) = 45e^{0.22*25} = 11,011\\\\Year \: 2050 = P(30) = 45e^{0.22*30} = 33,079\\\\[/tex]
Therefore, the starting population of ewoks was 45 in 2020 and increased to 33,079 by 2050 in a time span of 30 years.
