You can model the population of a certain city between 1945-2000 by the radical function P(x) = 55,000 sqrt x - 1,945. Using this model, in which year was the population of that city 165,000?

Question

You can model the population of a certain city between 1945-2000 by the radical function P(x) = 55,000 sqrt x - 1,945. Using this model, in which year was the population of that city 165,000?

A) 1948
B) 1951
C) 1954
D) 1957

Answer 1

We need to solve the equation 55,000 sqrt(x) - 1,945 = 165,000 for x (year).

Starting with the equation:
55,000 sqrt(x) - 1,945 = 165,000
55,000 sqrt(x) = 166,945
sqrt(x) = 166,945 / 55,000
sqrt(x) = 3.035

Now, we need to square both sides to solve for x:
x = 3.035^2
x = 9.212275

Converting this into a year between 1945-2000, we see that the population was 165,000 in 1954.

So, the answer is C) 1954.