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

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

1. 👍
2. 👎
3. 👁
1. 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

1. 👍
2. 👎

Similar Questions

1. Algebra II Help

4) The function f(x)=2(3)^x represents the growth of a dragonfly population every year in a remote swamp. Rose wants to manipulate the formula to an equivalent form that calculates seven times a year, not just once a year. Which

2. Economics

1) Which of the following is an example of a measure of labor productivity? a. Autos get 30 gallons to the mile. b. The growth rate of per capita real GDP is 3.5 percent per year. c. Farm workers produce 30 bushels of wheat per

3. Personal Finance

Check my work pls. 1. The components of ___ are variable costs and fixed costs. A. Entire cost B. Total cost* C. Complete cost D. Required cost 2. What is the margin of safety? A. How much sales can fall before a business starts

4. Math

A certain type of bacteria is growing at an exponential rate that can be modeled by the equation y=ae^kt, where t represents the number of hours. There are 300 bacteria initially, and 1500 bacteria 5 hours later. Find the rate of

1. 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

2. Calculus

A rectangle has width w inches and height h, where the width is twice the height. Both w and h are functions of time,t, measured in seconds. If A represents the area of the rectangle, what is the rate of change of A with respect

3. Math

A population doubles every 18 years. Assuming exponential growth find the following: (a) The annual growth rate: (b) The continuous growth rate is

4. Algebra

The exponential function f(x) = 3(5)x grows by a factor of 25 between x = 1 and x = 3. What factor does it grow by between x = 5 and x = 7? A) 5 B) 25 C) 125 D) 625 3) If a city that currently has a population of 1000 triples in

1. precalculus

A population doubles every 30 years. Assuming exponential growth find the following: annual growth rate: % continuous growth rate: %

2. Algebra

which of following best define the two quantities that are measure to find the call rate phone company? A.the quantity of price measured in dollars depends on the quantity of time measured in minutes B. the quantity measured in

3. calculus

A right triangle has base x feet and height h feet, where x is constant and h changes with respect to time t, measured in seconds. The angle θ, measured in radians, is defined by tanθ=h/x. Which of the following best describes

4. MATHEMATICS

it has been observed that a particular plant's growth is directly proportional to time. it measured 2 cm when arrived at the nursery and 2.5 cm exactly one week later. if the plant continues to grow at this rate, determine the