nobody is answering this b) for 0 less than or equal to t less than or equal to 7, must there be a time when W9t) =18? Explain

Question

t (minutes)--> 0 1 2 4 6 7

W(t) (ounces)--> 0 8 13 22 25 33

water is dripping into a cup. The amount of water in the cup at time t, 0 less than or equal to t which is less than or equal to 6, is given by the differentiable function W, where t is measured in minutes. Selected values of W(t), measured in ounces are given in the table above.

b) for 0 less than or equal to t less than or equal to 7, must there be a time when W9t) =18? Explain

c) for t>7, water leaks out of the cup at a constant rate of 0.2 ounces per minute. At what time will there be no water left in the cup?

Answer 1

b. Since W(t) is differentiable, it must also be continuous.

W(2) = 13 < 18 and W(4) = 22 > 18. So, by the Intermediate Value Theorem, there must be a real number, c, between 2 and 4 such that W(c) = 18.