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Mathematics
Mathematics
Problem
A flow-rate model for water entering a reservoir is given by
F
(
t
)
=
{
60
t
,
0
≤
t
<
2
,
k
t
2
,
2
≤
t
≤
4
,
F(t)=\begin{cases} 60t, & 0\le t<2,\\ kt^{2}, & 2\le t\le4, \end{cases}
F
(
t
)
=
{
60
t
,
k
t
2
,
0
≤
t
<
2
,
2
≤
t
≤
4
,
where
t
t
t
is measured in hours and
F
(
t
)
F(t)
F
(
t
)
in liters per hour. Determine the value of
k
k
k
that makes
F
F
F
continuous on
[
0
,
4
]
[0,4]
[
0
,
4
]
.
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