You can model the population of a certain city between 1945-2000 by the radical function
P(x) = 55,000 /x - 1,945. Using this model, in which year was the population of that city
165,000? (1 point)
1948
• 1951
• 1954
• 1957
Where / means square root
To find which year the population was 165,000, we can set up the equation:
P(x) = 165,000
165,000 = 55,000 / √x - 1,945
Now, we can solve for x:
165,000 = 55,000 / √x - 1,945
√x - 1,945 = 55,000 / 165,000
√x - 1,945 = 1/3
√x = 1/3 + 1945
√x = 1945 + 1/3
√x = 1945 + 0.3333
√x = 1945.3333
Now, we can square both sides to solve for x:
x = (1945.3333)^2
x ≈ 3782
So, the year 3782 corresponds to a population of 165,000 in the model equation provided. However, since we are looking for the year between 1945-2000, the year 3782 is not within the given time frame.
Therefore, based on the options provided, the closest year to when the population was 165,000 is 1954.