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

(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.