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Total Chapter 12 bankruptcy filings between 1996 and 2000 can be modeled asBt)-83.9t+ 1063where t is the number of years since 1996.t(a) Is the rate of change positive, negative, or neither?O positiveonegativeO neitherIs the function increasing, decreasing, or neither?O increasingo decreasingO neither(b) What is the rate of change of the number of Chapter 12 bankruptcy filings?filings per year(c) Sketch a graph of the model.B(tВ(0)10001000800800600600400400200200144CВ(0)В(0)100010008008006006004004002002002342CWhat is the slope of the graph?(d) Find the output for which the input is three.Explain its significance in context. (Hint: Round to the context.)there wereIn the yearChapter 12 bankruptcy filings.

Question
Total Chapter 12 bankruptcy filings between 1996 and 2000 can be modeled as
Bt)-83.9t+ 1063
where t is the number of years since 1996.t
(a) Is the rate of change positive, negative, or neither?
O positive
onegative
O neither
Is the function increasing, decreasing, or neither?
O increasing
o decreasing
O neither
(b) What is the rate of change of the number of Chapter 12 bankruptcy filings?
filings per year
(c) Sketch a graph of the model.
B(t
В(0)
1000
1000
800
800
600
600
400
400
200
200
1
4
4
C
В(0)
В(0)
1000
1000
800
800
600
600
400
400
200
200
2
3
4
2
C
What is the slope of the graph?
(d) Find the output for which the input is three.
Explain its significance in context. (Hint: Round to the context.)
there were
In the year
Chapter 12 bankruptcy filings.
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Total Chapter 12 bankruptcy filings between 1996 and 2000 can be modeled as Bt)-83.9t+ 1063 where t is the number of years since 1996.t (a) Is the rate of change positive, negative, or neither? O positive onegative O neither Is the function increasing, decreasing, or neither? O increasing o decreasing O neither (b) What is the rate of change of the number of Chapter 12 bankruptcy filings? filings per year (c) Sketch a graph of the model. B(t В(0) 1000 1000 800 800 600 600 400 400 200 200 1 4 4 C В(0) В(0) 1000 1000 800 800 600 600 400 400 200 200 2 3 4 2 C What is the slope of the graph? (d) Find the output for which the input is three. Explain its significance in context. (Hint: Round to the context.) there were In the year Chapter 12 bankruptcy filings.

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check_circleAnswer
Step 1

The total chapter 12 bankruptcy filings between 1996 and 2000 is modeled as B(t) = -83.9t + 1063, where t is the number of years since 1996. So, the values of t are 0 for 1996, 1 for 1997, 2 for 1998, 3 for 1999 and 4 for 2000.

Step 2

Here,

В (1)-в (0)
(a) The rate of change of B(t)
1-0
979.1-1063
1
1
-83.9
So, the rate of change is negative.
Since the rate of change is negative the function is decreasing
(b) The rate of change of the total chapter 12 is -83.9 filling per year
(The calculation can be seen in the part (a))
help_outline

Image Transcriptionclose

В (1)-в (0) (a) The rate of change of B(t) 1-0 979.1-1063 1 1 -83.9 So, the rate of change is negative. Since the rate of change is negative the function is decreasing (b) The rate of change of the total chapter 12 is -83.9 filling per year (The calculation can be seen in the part (a))

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Step 3

(c)  Now, we need to draw the...

1200
1063
979.1
1000
895.2
811.3
727.4
800
600
400
200
0
0.5
1
1.5
2
2.5
3.5
4.5
t
So, the first option is correct
B(1)-B (0)
The slope of the graph is
1-0
979.1-1063
-83.9
help_outline

Image Transcriptionclose

1200 1063 979.1 1000 895.2 811.3 727.4 800 600 400 200 0 0.5 1 1.5 2 2.5 3.5 4.5 t So, the first option is correct B(1)-B (0) The slope of the graph is 1-0 979.1-1063 -83.9

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