Consider the following table. (Note: This exercise corresponds to the subsection Model Choices.)Production, Given the Amount Invested in CapitalCapital, x(million dollars)Production, P(billion units)62018372441304442594878(a) Describe the behavior suggested by a scatter plot of the data and list the types of models that exhibit this behavior.A scatter plot of the data is increasingto the left of x 24 and concave upand appears to have an inflection point near x = 24. The scatter plot is concave downto the right of x = 24. This behavior suggests a cubicfunction(b) Describe the possible end behavior as input increases and list the types of models that would fit each possibility.Production should decrease without bound as capital expenditure increases. A cubic, quadratic, logarithmic, or exponential model would fit this possibilityProduction should continue to increase without bound as capital expenditure increases. A cubic, quadratic, logarithmic, or exponential model would fit this possibility.would fit this possibility.Production should continue to increase to a limiting value as capital expenditure increases. A logisticProduction should approach 0 as capital expenditure increases. A logistic model would fit this possibility.(c) Write the function of the model that best fits the data of the production level in billion units, where x million dollars is invested in capital, with data from 6 S x48. (Round all numerical values to four decimal places.)P(x) 0.0020x3-0.1504x24.1175x0.1679(d) Write the function of the model that best exhibits the end behavior of the data of the production level in billion units, where x million dollars is invested in capital, with data from 6 s x48. (Round all numerical values to four decimal places.)P(x)

Question
Asked Sep 16, 2019

 i am having trouble with d)

Consider the following table. (Note: This exercise corresponds to the subsection Model Choices.)
Production, Given the Amount Invested in Capital
Capital, x
(million dollars)
Production, P
(billion units)
6
20
18
37
24
41
30
44
42
59
48
78
(a) Describe the behavior suggested by a scatter plot of the data and list the types of models that exhibit this behavior.
A scatter plot of the data is increasing
to the left of x 24 and concave up
and appears to have an inflection point near x = 24. The scatter plot is concave down
to the right of x = 24. This behavior suggests a cubic
function
(b) Describe the possible end behavior as input increases and list the types of models that would fit each possibility.
Production should decrease without bound as capital expenditure increases. A cubic, quadratic, logarithmic, or exponential model would fit this possibility
Production should continue to increase without bound as capital expenditure increases. A cubic, quadratic, logarithmic, or exponential model would fit this possibility.
would fit this possibility.
Production should continue to increase to a limiting value as capital expenditure increases. A logistic
Production should approach 0 as capital expenditure increases. A logistic model would fit this possibility.
(c) Write the function of the model that best fits the data of the production level in billion units, where x million dollars is invested in capital, with data from 6 S x
48. (Round all numerical values to four decimal places.)
P(x) 0.0020x3-0.1504x2
4.1175x0.1679
(d) Write the function of the model that best exhibits the end behavior of the data of the production level in billion units, where x million dollars is invested in capital, with data from 6 s x
48. (Round all numerical values to four decimal places.)
P(x)
help_outline

Image Transcriptionclose

Consider the following table. (Note: This exercise corresponds to the subsection Model Choices.) Production, Given the Amount Invested in Capital Capital, x (million dollars) Production, P (billion units) 6 20 18 37 24 41 30 44 42 59 48 78 (a) Describe the behavior suggested by a scatter plot of the data and list the types of models that exhibit this behavior. A scatter plot of the data is increasing to the left of x 24 and concave up and appears to have an inflection point near x = 24. The scatter plot is concave down to the right of x = 24. This behavior suggests a cubic function (b) Describe the possible end behavior as input increases and list the types of models that would fit each possibility. Production should decrease without bound as capital expenditure increases. A cubic, quadratic, logarithmic, or exponential model would fit this possibility Production should continue to increase without bound as capital expenditure increases. A cubic, quadratic, logarithmic, or exponential model would fit this possibility. would fit this possibility. Production should continue to increase to a limiting value as capital expenditure increases. A logistic Production should approach 0 as capital expenditure increases. A logistic model would fit this possibility. (c) Write the function of the model that best fits the data of the production level in billion units, where x million dollars is invested in capital, with data from 6 S x 48. (Round all numerical values to four decimal places.) P(x) 0.0020x3-0.1504x2 4.1175x0.1679 (d) Write the function of the model that best exhibits the end behavior of the data of the production level in billion units, where x million dollars is invested in capital, with data from 6 s x 48. (Round all numerical values to four decimal places.) P(x)

fullscreen
check_circleExpert Solution
Step 1

Given: -

Production, Given the Amount Invested in Capital
Capital, x
(million dollers)
Production, P
(billion units)
20
18
37
24
41
30
44
42
59
48
78
help_outline

Image Transcriptionclose

Production, Given the Amount Invested in Capital Capital, x (million dollers) Production, P (billion units) 20 18 37 24 41 30 44 42 59 48 78

fullscreen
Step 2

To find: -

Write the function of the model that best exhibits the end behavior of the
data of the production level in billion units, where x million dollars is
invested in capital, with data from 6sx<48
help_outline

Image Transcriptionclose

Write the function of the model that best exhibits the end behavior of the data of the production level in billion units, where x million dollars is invested in capital, with data from 6sx<48

fullscreen
Step 3

Calculation...

Let the equation of the function of the model be
Р(x) %3 а,х' + а,х* + а,х +а,.. (1)
Now
Put x6, so that p(x) = 20 in (1)
20 a, (6)a,(6) a,(6)+a
— 216а, +36а, + ба, +а,
20...(2)
Put x18, so that p(x) = 37in (1)
37 = a, (18)a, (18) a(18)+a
5832a, 324a, +18a, +a =37...(3)
Put 42 so that, p(x) = 59 in (1)
59 - а, (42)' + а, (42)* + а,(42) + а,
74088a, 1764a, +42a, +a = 59...(4)
Put x48 so that, p(x) = 78 in (1)
78 a,(48) a(48)^ + a(48)+a
110592a 2304a, 48a, a = 78. ....5)
help_outline

Image Transcriptionclose

Let the equation of the function of the model be Р(x) %3 а,х' + а,х* + а,х +а,.. (1) Now Put x6, so that p(x) = 20 in (1) 20 a, (6)a,(6) a,(6)+a — 216а, +36а, + ба, +а, 20...(2) Put x18, so that p(x) = 37in (1) 37 = a, (18)a, (18) a(18)+a 5832a, 324a, +18a, +a =37...(3) Put 42 so that, p(x) = 59 in (1) 59 - а, (42)' + а, (42)* + а,(42) + а, 74088a, 1764a, +42a, +a = 59...(4) Put x48 so that, p(x) = 78 in (1) 78 a,(48) a(48)^ + a(48)+a 110592a 2304a, 48a, a = 78. ....5)

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour*

See Solution
*Response times may vary by subject and question
Tagged in

Math

Calculus

Functions

Related Calculus Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: Solve the equation for all solutions in the interval [0,2?). cos(x/2)=(√3)/2 Express answer in radia...

A:  Find the solution of cos(x/2) = (√3)/2. Use inverse of cosine to find the angles:

question_answer

Q: 2x2+y2=2 x2-2y2+8=0 Solve nonlinear equations

A: The given non-linear equations are

question_answer

Q: Consider a point Q(x1, y1, z1) and a line L given by the vector equation r = r0 +tv,where r0 = &lt;x...

A: First obtain a, where a is the distance between R0 and Q.

question_answer

Q: what is the limit of x^4 plus x^5 as x approaches negative infinity?

A: Evaluate the limit of

question_answer

Q: Can you please help me step by step with this problem?

A: We can see, that the graph of the function given is a straight line and the slope of the line is pos...

question_answer

Q: 2#3 The boiling point of water, B, depends on the altitude above the sea level, A. Specifically, A (...

A: Part (a)Compare the given equation: B = (-10/3)A + 212 with the standard equation of a striaght line...

question_answer

Q: 88. A cell phone plan charges $49.95 per month plus $14.02 in taxes, plus $0.40 per minute for calls...

A: If the usage is less than or equal to 600 minutes.Then charges is (49.95+14.02)=$63.97

question_answer

Q: Because of past use of leaded gasoline, the concentration of lead in soil can be associated with how...

A: (a) Obtain the log model for the given data as follows.Let the log model be L(x) = A + Bln(x). Consi...

question_answer

Q: GRAPHS AND FUNCTIONS Graphing a piecewise-defined function: Problem type Suppose that the function g...

A: The function has a break at x = 3. We need to evaluate if the function is continuous at x = 3.