Question

The population of a certain town increases by $50$ percent every $50$ years. If the population in $1950$ was $810$, in what year was the population $160$?

• A. $1650$
• B. $1700$
• C. $1750$
• D. $1800$
• E. $1850$

Answer 1

The correct option is C $1750$

Increased by 50%= 1.5 times

$160\times {1.5}^n=810$

where,

n=number of 50 years period

${1.5}^n=\frac{81}{16}$

${\left(\frac{3}{2}\right)}^n=\frac{81}{16}={\left(\frac{3}{2}\right)}^4$

So,

$n=4$

So there will 4 50years period which means in year =$1950-(4\times 50)=1950-200=1750$ population was 160