1. If a stone is thrown down at 100 ft/sec from a height of 1000 feet, its heigh

Question

1. If a stone is thrown down at 100 ft/sec from a height of 1000 feet, its height after t seconds is given by

s=1000 - 100t - 16t^2

a) Find its average velocity over the period [1, 4].

     I found this answer at -180 ft/sec

b) Estimate its instantaneous velocity at time t = 4. how many feet per second?

2. For the given cost function, find the marginal cost at the given production level x.

    c(x) = 15,400 + 110x + 1000/x; x=100

    What's the cost per item?

3. A car wash firm calculates that its daily profit (in dollars) depends on the number n of workers it employs according to the given formula.

   P= -98n + 20n^2 - 0.005n^4

a) Calculate the marginal product at an employment level of 50 workers and interpret the result. $???

b) This means that, at an employment level of, HOW MANY 2, HOWHHworkers, the firm's daily profit will decrese at a rate of HOW MUCH per additional worker it hires. 3

Explanation / Answer

1) a) average velocity [1,4] = ( height at 1st sec - height at 4th sec) / (4 -1)

= (s(4) - s(1))/3 = 180 feet/s

1) b) For instantaneous velocity differentiate s with respect to t and put t = 4 in the function. The differentiated result is v = -100 - 32t = -228 feet/sec

2) For marginal cost, differentiate the cost function and put x= 100. Differentiated function is m(x) = 110 -1000/x^2 . now put x =100 to get m(100) = 109.9

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