word problem please help!

[msosebee]

The function w(x) = -0.01x2 + 0.27x + 8.6 can be used to estimate the number of self-employed workers in the United States, in millions, x years after 1980 (Source: United States Bureau of Labor Statistics). For what years were there (or will there be) 10.12 million self-employed working in the United States?

 

[mmm4444bot]

Function w is defined by a quadratic polynomial with a negative leading coefficient. Therefore, the graph of function w is a parabola that opens downward.

Think of the horizontal line y = 10.12 intersecting near the top of the parabola at two locations.

You need to find the two locations where w(x) = 10.12 because those two values of x define the requested interval.

Do you know how to use the Quadratic Formula ?

Please show your work, when you ask for help on these boards. Otherwise, nobody can determine where to begin helping you.

Cheers ~ Mark

 

[Deleted member 4993]

The function w(x) = -0.01x[sup:2srgw1rj]2[/sup:2srgw1rj] + 0.27x + 8.6 can be used to estimate the number of self-employed workers in the United States, in millions, x years after 1980 (Source: United States Bureau of Labor Statistics). For what years were there (or will there be) 10.12 million self-employed working in the United States?

Define what do you need to find .

In this case you need find 'x' - when w(x) = 10.12

Please show us your work, indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[msosebee]

sorry Im new
yea i have
-.27+/- (square root)-.2711 / .02

..i cannot figure out what to do with the square root of -.2711

 

[Mrspi]

sorry Im new
yea i have
-.27+/- (square root)-.2711 / .02

..i cannot figure out what to do with the square root of -.2711

I'm not sure how you came up with that.....

w(x) = -0.01x[supvedmmx5]2[/supvedmmx5] + 0.27x + 8.6 can be used to estimate the number of self-employed workers in the United States, in millions, x years after 1980

Ok...you are looking for the value of x (which will be the number of years after 1980 when the value of the function (number of self-employed workers) is 10.12 million.

Substitute 10.12 for w(x):

10.12 = -0.01x[supvedmmx5]2[/supvedmmx5] + 0.27x + 8.6

Since this is a quadratic equation, let's get one side to be 0. Subtract 10.12 from both sides:

10.12 - 10.12 = -0.01x[supvedmmx5]2[/supvedmmx5] + 0.27x + 8.6 - 10.12

0 = -0.01x[supvedmmx5]2[/supvedmmx5] + 0.27x - 1.52

Hmmmm...I'd sure like that equation a LOT better if the coefficient of x[supvedmmx5]2[/supvedmmx5] was POSITIVE, and if there were no decimals. Let's see...what if I multiply both sides by -100?

-100(0) = -100(-0.01x[supvedmmx5]2[/supvedmmx5] + (-100)(0.27x) - (-100)(1.52)

0 = x[supvedmmx5]2[/supvedmmx5] - 27x + 152

Now, apply the quadratic formula. You should NOT get a negative number under the radical sign...in fact, you'll get a VERY NICE number.

OH....and don't forget...."x" is the number of years AFTER 1980. So, whatever value(s) you get for x will need to be ADDED to 1980 to give you the year(s) when this number of workers are self-employed.

 

[mmm4444bot]

i have

[-.27+/- (square root)-.2711] / .02

Your value for the discriminant is wrong.

Your value for 2a is wrong.

b^2 - 4ac should be 0.4169. Please check your arithmetic.

Use a scientific calculator, to evalutate sqrt(0.4169) = 0.6457 (rounded).

2a should be -0.02.

 

[mmm4444bot]

For what years were there (or will there be) 10.12 million self-employed working in the United States?

Oops. I misread the sentence above to mean an interval. (i.e., I read it as somehow "10.12 million or more").

My earlier post is wrong, where I said that you need to find an interval.

The answer is only two specific years, as described by Mrs. Pi.