Posted by **Sarah** on Sunday, April 11, 2010 at 2:56pm.

The rate of growth of the profit is approximated by P'(x)=xe^(-x^2) where x represents time measured in years. The total profit in the third year that the new technology is in operation is $10,000.

1.Find the total profit function

2. what happens to the total amount of profit in the long run?

- Calculus -
**Reiny**, Sunday, April 11, 2010 at 3:43pm
If P'(x)=xe^(-x^2) , then

P(x) = (-1/2) e^(-x^2) + c

when t= 3 , P(3) = 10000

10000= (-1/2)e^(-9) + c

10000 = -.00006 + c

c = 10000.0000617

1. P(x) = (-1/2) e^(-x^2) + 10000.0000617

2. "in the long run" implies x --->∞

which means (-1/2) e^(-x^2) ---> 0

so P(∞) = 10000.0000617

## Answer this Question

## Related Questions

- Calculus - The rate of growth of the profit is approximated by P'(x)=xe^(-x^2) ...
- Calculus - The rate of growth of the profit is approximated by P'(x)=xe^(-x^2) ...
- Calculus - The rate of growth of the profit (in millions of dollars) from a new ...
- Calculus - he rate of growth of the profit from an invention is approximated by ...
- math b50 - must answered in sequences/series formulas If the profit earned by a ...
- Math - Wirte an exponential growth model. 22. A business had a $20,000 profit in...
- Calculus - Company QRS generated a net profit between 1992 and 1997 at a rate ...
- Economics - I got a lot of problems with this exercise. I really hope you can ...
- Algebra - A business owner opens one store in town A. The equation p(x)=10,000(1...
- economics - Samantha Roberts has a job as a pharmacist earning $30,000 per year...