From 1890 to 1990, the American Indian population P (in thousands) can be modeled by P = .005x^3 -.43x^2 +11.32x +212 when x is the number of years since 1890. During what year was the population 725,000?

Hint: Let P = 725 and get the equation = 0, then solve for x intercept. Window: x min = 0 for 1890, x max = 100 for 1990.

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We are given a model for the population `P(x)=.005x^3-.43x^2+11.32x+212` where x is the number of years since 1890, and P is in thousands. We are asked to find the year that the population was 725,000.

`725=.005x^3-.43x^2+11.32x+212`

`y=.005x^3-.43x^2+11.32x-513`

We use a graphing utility to find the zero(s) of this function: the graph

Since the function is a cubic, we know from the graph that there is only one zero. It is between 70 and 80. Using the zero calculator on a graphing utility we find `x~~74.12973`

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Thus the year the population was 725000 was 1890+74=1964.

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