Prison Population The following curve is a model of a certain country's total prison population as a function of time
Posted: Thu Jul 14, 2022 4:22 pm
Prison Population Thefollowing curve is a model of a certain country's total prisonpopulation as a function of time in years (yearssince 1990).
The t N-coordinate plane is given.The t-axis is labeled "Year," andthe N-axis is labeled "Number ofprisoners (millions)." A curve enters the window at (0,1.39), goes up and right becoming more steep, passesthrough (2.5, 1.45), passes through (5,1.53), goes up and right becoming less steep, passesthrough (6.5, 1.58), and exits the window at (10,1.62).
(a)
Which is correct?
Over the period [5, 10] the instantaneous rate of changeof N is increasing.Over the period [5, 10] theinstantaneous rate of change of N isdecreasing.
(b)
Which is correct?
The instantaneous rate of change of prison populationat t = 4 was less than the average rate ofchange over the interval [0, 10].The instantaneous rate ofchange of prison population at t = 4 was greaterthan the average rate of change over the interval [0,10]. The instantaneous rate of change ofprison population at t = 4 was approximatelyequal to the average rate of change over the interval [0,10].
(c)
Which is correct?
Over the period [0, 10] the instantaneous rate of changeof N is increasing, then decreasing.Over theperiod [0, 10] the instantaneous rate of changeof N is decreasing, thenincreasing. Over the period [0, 10] theinstantaneous rate of change of N is alwaysincreasing.Over the period [0, 10] the instantaneous rate of changeof N is always decreasing.
(d)
According to the model, this country's total prison populationwas increasing fastest around what year?
(e)
Roughly estimate the instantaneous rate of changeof N at
t = 4
by using a balanced difference quotient with
h = 1.5.
(Round your answer to three decimal places.)
million prisoners per year
Interpret the result.
In 1994, this country's total number of prisonerswas ---Select--- increasing decreasing ata rate of approximately prisoners per year.
The t N-coordinate plane is given.The t-axis is labeled "Year," andthe N-axis is labeled "Number ofprisoners (millions)." A curve enters the window at (0,1.39), goes up and right becoming more steep, passesthrough (2.5, 1.45), passes through (5,1.53), goes up and right becoming less steep, passesthrough (6.5, 1.58), and exits the window at (10,1.62).
(a)
Which is correct?
Over the period [5, 10] the instantaneous rate of changeof N is increasing.Over the period [5, 10] theinstantaneous rate of change of N isdecreasing.
(b)
Which is correct?
The instantaneous rate of change of prison populationat t = 4 was less than the average rate ofchange over the interval [0, 10].The instantaneous rate ofchange of prison population at t = 4 was greaterthan the average rate of change over the interval [0,10]. The instantaneous rate of change ofprison population at t = 4 was approximatelyequal to the average rate of change over the interval [0,10].
(c)
Which is correct?
Over the period [0, 10] the instantaneous rate of changeof N is increasing, then decreasing.Over theperiod [0, 10] the instantaneous rate of changeof N is decreasing, thenincreasing. Over the period [0, 10] theinstantaneous rate of change of N is alwaysincreasing.Over the period [0, 10] the instantaneous rate of changeof N is always decreasing.
(d)
According to the model, this country's total prison populationwas increasing fastest around what year?
(e)
Roughly estimate the instantaneous rate of changeof N at
t = 4
by using a balanced difference quotient with
h = 1.5.
(Round your answer to three decimal places.)
million prisoners per year
Interpret the result.
In 1994, this country's total number of prisonerswas ---Select--- increasing decreasing ata rate of approximately prisoners per year.