Answer:
The countries population in 2000 was 241,08 millions
Step-by-step explanation:
To resolve this exercise we need to know the exponential model:
[tex]P_(_t_)=P_0*e^k^t[/tex]
Where:
[tex]P_(_t_)[/tex]: The population in certain time
[tex]P_(_0_)[/tex]: Initial population
k: constant
t: time frame
With the problem information we can find the constant (k), because we have all the information in t=10 years (1990-1980=10 years)
[tex]P_(_1_9_9_0_)=P_(_1_9_8_0_)*e^k^1^0[/tex]
[tex]225m=210*e^1^0^k[/tex]
[tex]\frac{225m}{210m}=e^1^0^k[/tex]
We multiply by natural logarithm on both sides of this equation and we have:
[tex]Ln(\frac{15m}{14m})=10*k\\k=\frac{Ln\frac{15}{14}}{10}\\k=0.0069[/tex]
With the constant (k) we can find the population in 2000
[tex]P_(_0_)=210m[/tex]: Initial population
k=0.0069
t=20 years (2000-1980=20 years)
[tex]P_(_2_0_0_0_)=P_(_1_9_8_0_)*e^k^2^0[/tex]
[tex]P_(_2_0_0_0_)=210m*e^0^.^0^0^6^9^*^2^0[/tex]
[tex]P_(_2_0_0_0_)=210m*e^0^.^1^3^8[/tex]
[tex]P_(_2_0_0_0_)=210m*1.1479[/tex]
[tex]P_(_2_0_0_0_)=241.08m[/tex]
The countries population in 2000 was 241,08 millions
