3. Given the following data: 0.1 0.2 0.3 0.4 f(x) -0.29004986 -0.56079734 -0.81401972 -0.10100000 (a) Present this data in a divided difference table. (b) Construct a Newton's interpolating polynomial of degree 3 using this table. (c) Approximate f(0.15) and f (0.28) using (b) above.

3. Given the following data: 0.1 0.2 0.3 0.4 f(x) -0.29004986 -0.56079734 -0.81401972 -0.10100000 (a) Present this data in a divided difference table. (b) Construct a Newton's interpolating polynomial of degree 3 using this table. (c) Approximate f(0.15) and f (0.28) using (b) above.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...

See similar textbooks

Related questions

Q: Which of the following statements are true about the relationships of alpha and beta type of errors?…

A: Answer :- Alpha and beta errors are inversely proportional with one another There are main two…

Q: QI: From the following table find the value of f'(1.2), f'(1.7) andf'(2.1) X y 1.4 4.055 1.6 4.953…

Q: The table below shows the average monthly temperature in Wellington NZ from 1971 to 2000. The…

A: Given data: Month (t)Average monthly temperature (T),…

Q: Consider the following equation and figure. a = 50 y a y = f(x) 2a x (a) By reading values from the…

A: Given the graph of the function y=f(x). a. To find the area of the region under the graph of the…

Q: From a function, f(x), we obtain the following data points: (ri, f(x₂)) = {(-0.5, e³/2), (0, 1),…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Which of the following is true? (Intercept) unemp Estimate -6.7142 -1.0010 Std. Error t value 5.4567…

A: The 'unemp' coefficient is not significant, because the corresponding p-value, which is Pr>|t| is…

Q: 1. Determine the slope of the following functions. į. f(x) = 4x³ + 5x4 - 9x + 2 f(x) = sin(3x) - 5x³…

A: We determine the slope of the following functions. i. f(x) = 4x3 + 5x4 - 9x…

Q: Suppose the high tide in Seattle occurs at 1:00 a.m. and 1:00 p.m. at which time the water is 16…

A: The high tide in Seattle occurs at 1:00 a.m. and 1:00 p.m. at which time the water is 16 feet above…

Q: Given the following data: x 0.6 0.7 0.8 0.9 1.0 f(x) 5.2293 3.6155 2.7531 2.2717 2 Find the second…

A: Consider the given table. x0.60.70.80.91.0fx5.22933.61552.75312.27172 We have to find the second…

Q: 6. Find the derivative for each function. b. f(x) In 5x3 2)3 f(x) (e*3 2) а.

A: Use exponent rule for exponent 3 and use chain rule for (e^x^3 +2)

Q: Find the average rate of change of the function g(x)=√6+x from x= a to x=a+h. Simplify your answer…

A: Given queryis to find the average rate of change.

Q: 3. Use implicit differentiation to find y for t 2 2 y² + ²/x = 2x²y

A: given y2+7x=2x2ydxndx=nxn-1d dx(a.b)=adbdx+bdadx

Q: The table time (z.) 1 2 3 4 5 6 infections (y = f(x)) 32 37 34 48 53 69 depicts the number of newly…

A: We will be solving first three question as mentioned. The given table is: Time xi 1 2 3 4 5 6…

Question

3. Given the following data:
0.1
0.2
0.3
0.4
f(x) -0.29004986
-0.56079734
-0.81401972
-0.10100000
(a) Present this data in a divided difference table.
(b) Construct a Newton's interpolating polynomial of degree 3 using this table.
(c) Approximate f(0.15) and f (0.28) using (b) above.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Interpolation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
Repeat the previous exercise to find the formula forthe APY of an account that compounds daily. Usethe results from this and the previous exercise todevelop a function I(n)for the APY of any accountthat compounds n times per year.
Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?
Example 7.4. Using Newton's backward difference formula, construct an interpolating polynomial of degree 3 for the data : f(-0.75) = -0.0718125, f(-0.5) = -0.02475, f(-0.25) 0.5) - = 0.3349375, f(0) = 1.10100. Hence find f(-1/3). (Anna, B.Tech., 2003)
May you please answer letters a-c
Given the following data which generated by the function y = 1/x. 1 4 y=f(x) 1 0.5 0.3333 0.25 0.2 a. Approximate f(4.5) using first and second order Lagrange interpolating polynomial. b. Which method gives the highest accuracy? Discuss.
Show your computation and highlight your final answer.
Let f(x) be a function tabulated over 4 points, as shown in the table below. Using a degree 3 Newton interpolating polynomial, obtain an approximation for f(2.22). Fill in the table below with the values of the Split Differences up to order 3, as seen in the video lessons. Then enter the value obtained as an approximation of f(2.22) using the Newton polynomial of degree 3. Perform the calculations with 4 decimal places and rounding. Use comma as separator for fractional values (Ex: 3.145 instead of 3.145).
Sulphur dioxide is released into the atmosphere when coal is burnt .In a city the amount of sulphur dioxide was a maximum of 4.5 tons on July 1 and a minimum of 1.2 ton 26 weeks later. Let P=f(n) be the amount of sulphur dioxide released during the n -th week after July 1. What is the amplitude, vertical shift and period of the funtion P=f(n) and write down the formula of the funtion P=f(n).
The wind-chill index is modeled by the function W = 13.12 + 0.62157- 11.37v0.16 + 0.39657v0.16 where T is the temperature (°C) and v is the wind speed (in km/h). When T = -14°C and v= 35 km/h, by how much (in °C) would you expect the apparent temperature W to drop if the actual temperature decreases by 1°C? (Round your answers to two decimal places.) °C drop What if the wind speed increases by 1 km/h while the actual temperature stays constant at T = -14°C? °C drop
5. Given the following data: 0.0 0.2 0.4 0.6 0.8 f (x) -6.12500 -5.89173 -5.64215 -4.91321 -4.28757 (a) Complete the difference table for this data. (b) Using Newton's Forward -Difference Formula, approximate f(0.5). (c) Using Newton's Backward- Difference Formula, approximate f(0.65).
Letter B and C