You can model the population of a certain city between the years 1965 and 1995 by the radical function p of x equals seventy five thousand times the cubed root of x minus one thousand nine hundred forty. Using this model, in what year was the population of that city 245,000?

Question

You can model the population of a certain city between the years 1965 and 1995 by the radical function p of x equals seventy five thousand times the cubed root of x minus one thousand nine hundred forty. Using this model, in what year was the population of that city 245,000?

(1 point)
Responses

1973
1973

1975
1975

1979
1979

1970

Answer 1

The population equation p(x) = 75000∛(x - 1940) represents the population of the city in terms of the year x.

To find when the population was 245,000, we set p(x) = 245,000 and solve for x:

75000∛(x - 1940) = 245,000
∛(x - 1940) = 245000/75000
∛(x - 1940) = 3.2667
x - 1940 = 3.2667^3
x - 1940 = 33.576
x = 1973.576

The population of the city was 245,000 in the year 1973.