Question

You can model the population of a certain city between the years 1965 and 1995 by the radical function P(x)=75,000^3 SQRT x-1940 . Using this model, in what year was the population of that city 245,000?
a)1973
b)1975
c)1979
d)1970

Answer 1

The model is p(x) = 75,000 ∛(x - 1940)

Now use p(x) = 245,000 and solve for x

245,000 = 75,000 ∛(x - 1940) =

245,000 / 75,000 = ∛(x - 1940)

49/15 = ∛(x - 1940)

x - 1940 = [49/15]^3 = 34.86

x = 1940 + 34.86 = 1974.85

Then, the answer is 1975 (option b)