Question

You can model the population of a certain city between 1945-2000 by the radical function p(x)=55,000√x-1945. Using this model in which year was the population of that city 165,000?

Answer 1

165,000 = 55,000 sqrt x - 1945

find x:-

55000 sqrt x  = 166945
sqrt x = 166945/55000 = 3.035

x =   9.2

so required year = 1945 + 9 = 1954

Answer 2

Answer:

  In 1954 the population of the city became 165,000.

Step-by-step explanation:

Given : You can model the population of a certain city between 1945-2000 by the radical function $p(x)=55,000\sqrt{x-1945}$

To find : Using this model in which year was the population of that city 165,000?

Solution : The model of the function is

$p(x)=55,000\sqrt{x-1945}$

where p(x) is the population and x is the time (in years)

To find the year in which population reach 165,000

p(x)= 165,000, substitute the value in p(x)

$165000=55000\sqrt{x-1945}$

$\frac{165000}{55000}=\sqrt{x-1945}$

$3=\sqrt{x-1945}$

Squaring both side,

$3^2=(\sqrt{x-1945})^2$

$9=x-1945$

$x=1945+9$

$x=1954$

So, In 1954 the population of the city became 165,000.