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

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`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.

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