Question

The population of a city increases exponentially at a rate of $x\%$ every $5$ years.
In $1960$ the population was $60100.$
In $2015$ the population was $120150.$

Answer 1

$1960$ to $2015$

Number of years $=55$

and population increases every $5$ years

so time$=\frac{55}{5}$

$=11$

then,

$120150=60100{(1+\frac{x}{100})}^{11}$

$\frac{120150}{60100}={(1+\frac{x}{100})}^{11}$

$\sqrt[11]{111-999917}=1+\frac{x}{100}$

$1.0650371-1=\frac{x}{100}$

$x=0.0650371\times 100$

$x=6.50371\%$.