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.]
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.]
Births to Unmarried Mothers The percent of livebirths to unmarried mothers for the years 1970–2007can be modeled by the logistic functiony = 44.742/1 + 6.870e-0.0782xwhere x is the number of years after 1960.a. Use this model to estimate the percent in 1990 andin 1996.b. What is the upper limit of the percent of teenmothers who were unmarried, according to thismodel?
An evergreen nursery usually sells a certain shrub after 7 years of growth and shaping. The growth rate during those 7 years is approximated by...
The tuition in the school year 2012–2013 at a certain university was $15,000. For the school year 2017–2018, the tuition was $17,850. Find an exponential growth function for tuition T (in dollars) at this university t years after the 2012–2013 school year. (Round your values to four decimal places.)
T =
Assuming it increases at the same annual rate, use the function to predict the tuition (in dollars) in the 2021–2022 school year. (Round your answer to the nearest integer.)
$
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