GE Net Income 2007–2011 The annual net income of General Electric for the period 2007–2011 could be 8 approximated by P ( t ) = 1.6 t 2 − 15 t + 46 billion dollars ( 2 ≤ t ≤ 6 ) , Where t is time in year since 2005. GE net income ($ billions) a. Compute P ' ( t ) . How fast was GE’s annual net income changing in 2008? (Be careful to give correct units of measurement.) b. According to the model, GE’s annual net income (A) increased at a faster and faster rate (B) increased at a slower and slower rate (C) decreased at a faster and faster rate (D) decreased at a slower and slower rate during the first 2 years shown (the interval [ 2 , 4 ] ). Justify your answer in two ways: geometrically, reasoning entirely from the graph, and algebraically, reasoning from the derivative of P . [ HINT: See Example 4.]
GE Net Income 2007–2011 The annual net income of General Electric for the period 2007–2011 could be 8 approximated by P ( t ) = 1.6 t 2 − 15 t + 46 billion dollars ( 2 ≤ t ≤ 6 ) , Where t is time in year since 2005. GE net income ($ billions) a. Compute P ' ( t ) . How fast was GE’s annual net income changing in 2008? (Be careful to give correct units of measurement.) b. According to the model, GE’s annual net income (A) increased at a faster and faster rate (B) increased at a slower and slower rate (C) decreased at a faster and faster rate (D) decreased at a slower and slower rate during the first 2 years shown (the interval [ 2 , 4 ] ). Justify your answer in two ways: geometrically, reasoning entirely from the graph, and algebraically, reasoning from the derivative of P . [ HINT: See Example 4.]
Solution Summary: The author calculates the derivative P'(t) and the rate of change of General Electrical's net annual income in year 2008.
GE Net Income 2007–2011 The annual net income of General Electric for the period 2007–2011 could be 8 approximated by
P
(
t
)
=
1.6
t
2
−
15
t
+
46 billion dollars
(
2
≤
t
≤
6
)
,
Where t is time in year since 2005.
GE net income ($ billions)
a. Compute
P
'
(
t
)
. How fast was GE’s annual net income changing in 2008? (Be careful to give correct units of measurement.)
b. According to the model, GE’s annual net income
(A) increased at a faster and faster rate
(B) increased at a slower and slower rate
(C) decreased at a faster and faster rate
(D) decreased at a slower and slower rate during the first 2 years shown (the interval
[
2
,
4
]
). Justify your answer in two ways: geometrically, reasoning entirely from the graph, and algebraically, reasoning from the derivative of P. [HINT: See Example 4.]
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