Verified Answer :
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:
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.