# You can model the population of a certain city between the years of 1955 and 1995 by the radical function P(x)=80000∛(x-1940). Using the model, in what year was the population of that city 290,000

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted on

`P(x) = 80000(x-1940)^(1/3)`

P(x) is the population and x is the year which is between 1955 and 1995.

When population is 290000 then `P(x) = 290000`

`P(x) = 80000(x-1940)^(1/3)`

`290000 = 80000(x-1940)^(1/3)`

`290000/80000 = (x-1940)^(1/3)`

`3.625 = (x-1940)^(1/3)`

`3.625^3 = (x-1940)`

`x = 1987.6`

So the population of the city will be 290000 in the year of 1987.

Sameera W | (Level 1) eNoter

Posted on

lets correct the question first, I guess function should be as follows

P(x) =80000∛(x-1940)

P(x) is the city population in a certain year. so, in year x P(x)= 290000

from the equation

P(x)= 290000 =80000∛(x-1940)

290000/80000 =∛(x-1940)

3.625=∛(x-1940)

3.625^3=x-1940

47.63=x-1940

47.63+1940=x

1987.6 =x

so that, in1987 the population will be 290,000

so the answer is YEAR 1987