# 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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Expert Answers

jeew-m | Certified Educator

`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.*

Student Comments

Sameera W | Student

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

P(x) =80000∛(x-1940)

ANSWER

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**