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A metal ball at 15 °C is dropped into a large tank of… | StemPy Lab
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A metal ball at 15 °C is dropped into a large tank of water at 40 °C. The ball follows Newton's law of cooling with a positive constant k. Which equation gives its temperature T?
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High School (11–12)
Functions and Calculus › Differential Equations
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StemPy Lab
A metal ball at
15
∘
C
15\ ^\circ\text{C}
15
∘
C
is dropped into a large tank of water at
40
∘
C
40\ ^\circ\text{C}
40
∘
C
. The ball follows Newton's law of cooling with a positive constant
k
k
k
. Which equation gives its temperature
T
T
T
?
d
T
d
t
=
−
k
T
\dfrac{dT}{dt} = -kT
d
t
d
T
=
−
k
T
d
T
d
t
=
−
k
(
40
−
T
)
\dfrac{dT}{dt} = -k(40 - T)
d
t
d
T
=
−
k
(
40
−
T
)
d
T
d
t
=
k
(
40
−
T
)
\dfrac{dT}{dt} = k(40 - T)
d
t
d
T
=
k
(
40
−
T
)
d
T
d
t
=
k
(
T
−
15
)
\dfrac{dT}{dt} = k(T - 15)
d
t
d
T
=
k
(
T
−
15
)
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