Water is added to a storm water retention pond during a heavy rainstorm at the following rate in gallons per minute: R(t)=et, for 0 < t < 5 = 50e-0.2t, for 5 ≤ t < 15 Water exits the storm water retention pond into a stream at the following rate in gallons per minute: S (t) = for 0 < t < 15 " In(t+9) a) Is R continuous at t = 5? Show the work that leads to your answer. b) Find the average rate of change of S (t) over the interval 0 < t < 3. Using correct units, explain he meaning of that value in the context of this problem.
Water is added to a storm water retention pond during a heavy rainstorm at the following rate in gallons per minute: R(t)=et, for 0 < t < 5 = 50e-0.2t, for 5 ≤ t < 15 Water exits the storm water retention pond into a stream at the following rate in gallons per minute: S (t) = for 0 < t < 15 " In(t+9) a) Is R continuous at t = 5? Show the work that leads to your answer. b) Find the average rate of change of S (t) over the interval 0 < t < 3. Using correct units, explain he meaning of that value in the context of this problem.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Water is added to a storm water retention pond during a heavy rainstorm at the following rate in
gallons per minute:
R(t)=et, for 0 < t < 5
= 50e
S (t):
-0.2t
-
2
Water exits the storm water retention pond into a stream at the following rate in gallons per minute:
t
24
"
In(t+9)
for 5 < t < 15
(a) Is R continuous at t
=
for 0 < t < 15
5? Show the work that leads to your answer.
(b) Find the average rate of change of S (t) over the interval 0 < t < 3. Using correct units, explain
the meaning of that value in the context of this problem.
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