The rate of growth of profit in millions from an invention is approximated by P'(x)=xe^(-x^2), where x represents time in years. The total profit in year 1 from the invention is $20,000. Find the total profit function P(x), round to to the nearest thousandth if necessary.

Question

lukecrayonz · Answer

@Isaiah.Feynman

lukecrayonz · Answer

I know the integral is (-1/2)e^(-x^2)+C but now what?:(

lukecrayonz · Answer

@Luigi0210

luigi0210 · Answer

Set the original equal to the total and solve for C..so:
$$\LARGE 20,000=-\frac{1}{2}e^{(-x^2)}+C$$

luigi0210 · Answer

And x is the number of years, so x=1 in this case if I'm not mistaken

lukecrayonz · Answer

Right and I get the wrong answer :P

luigi0210 · Answer

oh, dang it ;-;

lukecrayonz · Answer

is it -204000, -0.204, 204000 or 0.204?

luigi0210 · Answer

Well I kind of doubt that they could have negative profit..

shamil98 · Answer

Did you integrate it correctly?

shamil98 · Answer

Because after setting the equation (after integrated) to 20000 and inputting x = 1, you should get the right answer...

luigi0210 · Answer

I think I'm doing it wrong.. sham.. maybe wrong method/equation? .-.

lukecrayonz · Answer

http://gyazo.com/73f0e8918126726b74d9eca60bcc90ff

lukecrayonz · Answer

@Directrix

lukecrayonz · Answer

Someoneeee:( haha

lukecrayonz · Answer

I got it, it's 0.204 because it's in millions.

b87lar · Answer

The issue is that the original problem says: the rate of change *in millions*

lukecrayonz · Answer

^ :)

b87lar · Answer

great minds think alike ;)