calculus

find the average value of the function
i=15[1-e^(-1/2t)] from t=0 to t=4

A. 7.5(1+e^-2)
B. 7.5(2+e^-2)
C. 7.5(2-e^-2)
D. 7.5(3-e^-2)

asked by Tracy
  1. average value is the integral divided by the interval length. Thinking in terms of area, the integral is the total area, and a rectangle with that same area would have width of the interval, height the average value

    Int(15 - 15e^(-t/2))[0,4]
    = 15t + 30e^(-t/2)[0,4]
    = (15*4 + 30/e^2) - (0 + 30)
    = 60 + 30/e^2 - 30
    = 30(1 + 1/e^2)

    Average value = 7.5(1 + 1/e^2) = A

    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. Maths

    Demand function P=50-Q Average Cost 5Q + 40 +10/Q Calculate the firm's total cost function Find the marginal cost function and evaluate it at Q=2 and Q=3 What is the total revenue function Find the firms's revenue maximising
  2. Calculus

    Find the average value of the function f(x) 8x^2-9x+8 on the interval [3,5]. Find the value of the x-coordinate at which the function assumes it's average value The average value is ? the x-coordinate is ? Please help and showing
  3. math

    Let the total cost function C(x) be defined as follows. C(x) = 0.0008x3 - 0.04x2 + 99x + 4400 Find the average cost function C. C(x) = ?? Find the marginal average cost function C '. C '(x) = ??
  4. Math

    An instructor gives regular 20-point quizzes and 100-point exams in a mathematics course. Average scores for six students, given as ordered pairs (x,y) where x is the average quiz score and y is the average test score, are (18,
  5. Calculus

    Find the average value of the function over [1,3] and all values of x in the interval for which the function: f(x)= 4(x^2+1)/x^2 equals its average value.
  6. math

    Find the average cost function C associated with the following total cost function C. C(x) = 0.000007x3 - 0.06x2 + 110x + 76000 C(x) = ?? (a) What is the marginal average cost function C' ? C'(x) = ?? (b) Compute the following
  7. calculus

    Find the average value of the function f(x)=8x^2-5x+6 , on the interval [3,5]. Find the value of x-coordinate at which the function assumes it's average value. what is the average value = to ? what is the x coordinate = to ?
  8. pre-cal: graphs of functions- fill in the blank

    To find the domain of a function from its graph... To find the range of a function from its graph... To approximate the relative minimum or maximum of a function using a graphing utility,... Let a(,f(a)) and (b,f(b)) be two points
  9. Calculus

    I'm supposed to find the average value of the function over the given interval. f(x) = sin(nx), interval from 0 to pi/n, where n is a positive integer. I know the average value formula, and I know that the integral of that
  10. Math (UBC)

    Economists use production functions to describe how output of a system varies with another variable such as labour or capital. For example, the production function P(L) = 200L + 10L^2 - L^3 goves the output of a system as a
  11. Math Calculus

    Economists use production functions to describe how output of a system varies with another variable such as labour or capital. For example, the production function P(L) = 200L + 10L^2 - L^3 goves the output of a system as a

More Similar Questions