<em><u>Complete Question:</u></em>
You can model the population of a certain city between 1955-2000 by the radical function
P(x) = 55,000 sqrt x-1945
Using this model, in which year was the population of that city 275,000?
<em><u>Answer:</u></em>
In 1970 population of that city is 275,000
<em><u>Solution:</u></em>
Given that,
<em><u>You can model the population of a certain city between 1955-2000 by the radical function
:</u></em>
![P(x) = 55000\sqrt{x - 1945}](https://tex.z-dn.net/?f=P%28x%29%20%3D%2055000%5Csqrt%7Bx%20-%201945%7D)
To find: year in which was the population of that city 275,000
Therefore,
x = ?
P(x) = 275000
Thus we get,
![275000 = 55000\sqrt{x - 1945}\\\\Divide\ both\ sides\ by\ 55000\\\\\frac{275000}{55000} = \sqrt{x-1945}\\\\5 = \sqrt{x - 1945}\\\\Take\ square\ on\ both\ sides\\\\25 = x - 1945\\\\x = 1945 + 25\\\\x = 1970](https://tex.z-dn.net/?f=275000%20%3D%2055000%5Csqrt%7Bx%20-%201945%7D%5C%5C%5C%5CDivide%5C%20both%5C%20sides%5C%20by%5C%2055000%5C%5C%5C%5C%5Cfrac%7B275000%7D%7B55000%7D%20%3D%20%5Csqrt%7Bx-1945%7D%5C%5C%5C%5C5%20%3D%20%5Csqrt%7Bx%20-%201945%7D%5C%5C%5C%5CTake%5C%20square%5C%20on%5C%20both%5C%20sides%5C%5C%5C%5C25%20%3D%20x%20-%201945%5C%5C%5C%5Cx%20%3D%201945%20%2B%2025%5C%5C%5C%5Cx%20%3D%201970)
Thus, in 1970 population of that city is 275,000