Question

The population of a coty is 100,000 and the annual growth rate is 4.2%. Write an equation to model the population y after x years

Answer 1

Answer: $1,00,000(1+0.042)^x$

Step-by-step explanation:

Given

The initial population of a city is $P_o=1,00,000$

The annual growth rate is $4.2\%$

after 1 year it is

$\Rightarrow P_1=1,00,000+4.2\%\times 1,00,000\\\Rightarrow P_1=1,00,000(1+0.042)$

after 2 years, it is

$\Rightarrow 1,00,000(1+0.042)+4.2\%\times 1,00,000(1+0.042)\\\Rightarrow 1,00,000(1+0.042)^2$

after x years it is

$\Rightarrow P_x=1,00,000(1+0.042)^x$