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 population of the city was 245,000 in the year 1950.

Step-by-step explanation:

To find the year when the population was 245,000, we need to solve the equation P(x) = 245,000. The given function is P(x) = 75,000 * square root(x - 1940). Let's plug in 245,000 for P(x) and solve for x:

245,000 = 75,000 * square root(x - 1940)

Divide both sides of the equation by 75,000:

3.27 = square root(x - 1940)

Square both sides of the equation to eliminate the square root:

10.6929 = x - 1940

Add 1940 to both sides of the equation:

x = 1950.6929

So, the population of the city was 245,000 in the year 1950. Therefore, none of the answer choices provided (a, b, c, d) is correct.

Answer 2

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)