1. A ball's position, in meters, as it travels every second is represented by the position function s(t) = 4.9t2+ 450.What is the velocity of the ball after 5 seconds? with units2.The cost in dollars of producing x units of a particular camera is C(x) = x2 – 10000. Find the average rate of change of C with respect to x when the production level is changed from x = 100 to x = 101. Include units in your answer.Find the instantaneous rate of change of C with respect to x when x = 100. Include units in your answer.
Accepted Solution
A:
1) The ball's position is described by: s(t) = 4.9t² + 450 We want to find the velocity, which is the 1st-order derivative of the displacement function (I assume this is an introductory calculus class) s'(t) = v(t) = 9.8t We get this by multiplying 4.9 x 2 and reducing the exponent by 1. Now we simply plug 5 in for t. v(5) = 9.8* 5 v(5) = 49m/s
2) Our cost function is C(x) = x² - 10,000 To find the average rate of change between these units, we use this formula: ( C(101) - C(100) ) ÷1 . We find the change in C, and divide by the change in x, which is just one. C(101) = 101² - 10,000 C(101) = 201
C(100) = 100² - 10,000 C(100= 0
C(101) - C(100) = 201 Average rate of change in cost is 201 dollars/ unit between the two points.