Use the Newton forward difference formula to construct interpolating polynomials of degree three for the following data. Approximate f(–0.3) f(-0.75) = -0.0718, f(-0.5) = -0.0247, f(-0.25) = 0.3349, f(0) = 1.1010

The rate of change of an autocatalytic chemical reaction is kQxkx2 where Q is the amount of the original substance, x is the amount of substance formed, and k is a constant of proportionality. Factor the expression.

The function f(s) = 400 + 0.0066667s2 – 0.0000001s4 approximates the length of the cable between the two vertical towers of a suspension bridge, where s is the sag in the cable. Estimate the length of the cable of the bridge in the next column if the sag is 28.3 feet. (Round your answer to the nearest foot.) ft 400 ft

A stock analyst plots the price per share of a certain common stock as a function of time and finds that it can be approximated by the -0.071 function S(t)=26+28c where t is the time (in years) since the stock was purchased. Find the average price of the stock over the first six years. The average price of the stock is $. (Round to the nearest cent as needed.)

On a certain winter day, the temperature of a northern city from 6 a.m. to 6 p.m. can be modeled by the function T(x) = -0.3x² - 8.6x - 2.3 where T(x) is the temperature (in degrees Celsius) and x is the number of hours after 6 a.m. Which of the following expressions would give the average temperature of the city between 8 a.m. (x = 2) and 3 p.m. (x = 9)? 9 (-0.12³ (-0.1x³-4.3x² - 2.3x) dx 9 © ¦ / (-0.12³ 4.3x² - 2.3x) dx 9 (-0.3x² -8.6x - 2.3) dr (-0.3x² -8.6x - 2.3) de

The function​ A(s) given by ​A(s)=0.245s+51 can be used to estimate the average age of employees of a company in the years 1981 to 2009. Let​ A(s) be the average age of an​ employee, and s be the number of years since​ 1981; that​ is, s=0 for 1981 and s=9 for 1990. What was the average age of the employees in 2003 and in​ 2009?

For each year, t, the population of a forest of trees, call it Forest A, is represented by the function A(t) = 85(1.026)*. In a neighboring forest, call it Forest B, the population of the same type of tree is represented by the function B(t) = 113(1.021)*. Do the functions represent growth or decay? Which forest has a larger growth or decay factor? Which forest had a greater number of trees initially? In a third forest, call it Forest C, the population of the same type of tree is represented by the function C(t) = 123 + (2.3)t. Is the function for Forest C linear, exponential, or neither?

Find T(10) and T(40). You may use a calculator.

Evaluate the function f(x) at the given numbers (correct to six decimal places). x² - 4x x²-x-12 f(x) = f(4.5) = 3/5 f(4.1) = 41/71 f(4.05) = 27/47 f(4.01) = 401/701 f(4.005) = 267/467 f(4.001) = 4001/7001 f(3.9) = 13/23 f(3.95) 79/139 f(3.99) = 133/233 f(3.995) 799/1399 f(3.999) = 1333/2333 = x = 4.5, 4.1, 4.05, 4.01, 4.005, 4.001, 3.9, 3.95, 3.99, 3.995, 3.999 I Guess the value of the limit of f(x) as x approaches 4, correct to six decimal places. (If an answer does not exist, enter DNE.) x² - 4x lim x→4 x² - x - 12 = 0.571367 X

The annual number of cars and trucks sold by a dealership can be modeled by the functions given below where x is the number of years since 2000. Fi Cars sold: c(x) =1.118x³ – 22.1492x +95.2693x +1210.7673 Trucks sold: t(x)=1.5964x³ - 36.4112x +200.5798x+476.9031 56. Write a function, T(x), that models the total annual number of cars and trucks sold. A) T(x)=2.7144x³ – 58.5604x² +295.8491x +1687.6704 6. B) T(x) =0.4784x³ –14.262x +105.3105x-733.8542 C) T(x) =2.7144x – 58.5604x² +105.3105x +733.7642 Cho D) T(x)=-0.4784x° +14.262x² – 105.3105x +733.8642 A) { 57. Write a function, D(x), that models how many more cars than trucks were sold annually. AB) A) D(x)=2.7144x³ +58.5604x +295.8491x +1687.6704 B) D(x) =0.4784x' -14.262x? +105.3105x -733.8642 C) D(x)=2.7144x³ – 58.5604x² +105.3105x+733.7642 Fi D) D(x)=-0.4784x³ +14.262x² – 105.3105x+733.8642 58. According to the model, how many cars and trucks were sold in 2009? (Round to nearest whole number.) 6. 59. According to the model, how many…