Calculus

posted by .

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 -

dp/dt = t e^-t^2

if p = c - .5e^-t^2
p' = t e^-t^2 =

when t = 3
10,000 = c - .5e^-9
c = 10,000 + .5 e^-9
c = 10,000 + .0000617
so
p = 10,000 - .5/ e^(t^2) essentially

It becomes 10,000 as t---> oo

Similar Questions

1. Calculus

The rate of growth of the profit (in millions of dollars) from a new technology is approximated by P'(x)=xe^(-x^2) Where x represents time measured in years. The total profit in the thrid year that the new technology is in operation …
2. Calculus

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 …
3. Calculus

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 …
4. math b50

must answered in sequences/series formulas If the profit earned by a company is \$100 in the first year, and doubles each year such that the profit earned in the second year is \$200, \$400 in the third year and so on. Find the total …
5. Calculus

Company QRS generated a net profit between 1992 and 1997 at a rate approximated by 20 t + 264.5 million dollars per year, where t is the time in years since 1992. Find the value, in 1992, of QRS's net profit over the 5-year period …
6. college algebra

A magazine company had a profit of \$98,000 per year when it had 32,000 subscribers. When it obtained 35,000 subscribers, it had a profit of \$117,500. Assume that the profit P is a linear function of the number of subscribers s. a.) …
7. Math

Wirte an exponential growth model. 22. A business had a \$20,000 profit in 1990. Then the profit increased by 20% per year for the next 10 years. y=c(1+r)^t y=20,000(1+0.2)^10 Is that correct?
8. Calculus

he rate of growth of the profit from an invention is approximated by P'(x)=xe^-x^2, where x represents time measured in years. The total profit in year 1 that the invention is in operation is \$15,000. Find the total profit function. …
9. Algebra

A business owner opens one store in town A. The equation p(x)=10,000(1.075)^t represents the anticipated profit after t years. The business owner opens a store in town B six months later and predicts the profit from that store to increase …
10. math

A new computer software company earns a profit of \$245 000 in its first year. The company expects the profit to increase by 15% each year for each subsequent year. (a) What profit can the company expect to earn in its seventh year?

More Similar Questions