Respuesta :
Answer:
The total percentage increase in the country's population over the three year period is 7.6%.
Step-by-step explanation:
Let x be the original population of a country.
It is provided that the population increased by 3%, 2.6%, and 1.8% in three successive years.
Compute the population of the country after three years as follows:
[tex]\text{New Population}=\text{Origibal Population}\times I_{1}\%\times I_{2}\%\times I_{3}\%[/tex]
[tex]=x\times [1+\frac{3}{100}]\times [1+\frac{2.6}{100}]\times [1+\frac{1.8}{100}]\\\\=x\times 1.03\times 1.026\times 1.018\\\\=1.07580204\cdot x\\\\\approx 1.076\cdot x[/tex]
The new population after three years is 1.076 x.
Compute the total percentage increase in the country's population over the three year period as follows:
[tex]\text{Total Increase}\%=\frac{\text{New Population}\ -\ \text{Original Population}}{\text{Original Population}}\times 100[/tex]
[tex]=\frac{1.076x-x}{x}\times 100\\\\=0.076\times 100\\\\=7.6\%[/tex]
Thus, the total percentage increase in the country's population over the three year period is 7.6%.
