Question

(b) locate the discontinuities of t. (enter your answers as a comma - separated list. if an answer does not exist, enter dne.)
classify the discontinuities as removable, jump, or infinite.
removable
jump
infinite
none - t is continuous
discuss the significance of the discontinuities of t to someone who uses the road.
the function is continuous, so there is no significance.
because of the sudden jumps in the toll, drivers may want to avoid the higher rates between t = 0 and t = 7, between t = 10 and t = 16, and between t = 19 and t = 24 if feasible.
because of the steady increases and decreases in the toll, drivers may want to avoid the highest rates at t = 7 and t = 24 if feasible.
because of the sudden jumps in the toll, drivers may want to avoid the higher rates between t = 7 and t = 10 and between t = 16 and t = 19 if feasible.
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Explanation:

Step1: Identify discontinuity points

Discontinuities occur where there are jumps in the graph. From the graph, the function has jumps at \(t = 7\), \(t=10\), \(t = 16\), \(t=19\).

Step2: Classify the discontinuities

Since the function has jumps at these points, they are jump - discontinuities.

Step3: Discuss significance

The sudden jumps in the toll (represented by the function \(T\)) mean that drivers may want to avoid the higher - rate intervals. The higher - rate intervals are between \(t = 7\) and \(t = 10\) and between \(t = 16\) and \(t = 19\).

Answer:

\(t = 7,10,16,19\)
jump
Because of the sudden jumps in the toll, drivers may want to avoid the higher rates between \(t = 7\) and \(t = 10\) and between \(t = 16\) and \(t = 19\) if feasible.