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 heat index (HI) is an estimate of the temperature felt by the human body based on the actual measured air temperature T (in °F) and relative humidity h,. It is given by HI = - 42.379 + 2.049015237 + 10.14333127h, – 0.22475541Th, – (6.83783 × 10-³)T² - (5.481717 x 10-3)h,² + (1.22874 × 10-³)7°h, + (8.5282 - 10-4)Th,² - (1.99 x 10-")T®h,?. a. If the air temperature in your area is 107°F with a relative humidity of 8%, how hot does your body feel? b. If the air temperature and relative humidity is known to be increasing at a rate of 2°F per sec and 1% per sec, resp., how fast is the heat index changing at the moment when the air temperature in your area is 107°F with a relative humidity of 8%?

The accounting team at a manufacturing business developed a model for the company's profit over its first year of business. Their profit, in thousands of dollars, followed the graph of p(t)= (1/6)t3-t2+t where t is the number of months since January 1st.  Use the mean value theorem to find the month in which the profits changed at the same rate as the average rate of change during the first 7 months. Midnight on New Year’s Eve corresponds to t=0,so for purposes of the mean value theorem, the first six months of the year correspond to the interval [0, 7].  Hint: Discard any solutions that are not in the corresponding open interval.  Note: Use a calculator to determine the solution. Write your answer as the name of the month, not a number. For example, the value t=2.3 corresponds to some time in March, so you would say the answer is "March."

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?

a cylindrical tank with a diameter of 20 feet is filled with oil to a depth of 40 feet. The oil begins draining at a constant rate of 2 cubic feet per second. write the volume of the oil remaining in the tank t seconds later as a function of t

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

Suppose a car drives north on I-95 starting from Miami. Let f(t) denote thenumber of miles from Miami to the car after t hours. What is the significanceof the difference quotient  f(5) − f(3)/5 − 3,and in what units is it measured?

Suppose you plan to upgrade a new phone when your IPhone X loses half of its value. Use P(t) to determine algebraically in how many months this will happen. Show all work.  P(t)=720(.9692)t

for a function f, the forward-divided differences are given by 1, 0.0 X = 0,4 /l, xal= 10 = 0.7 tal = 6 Determine the missing entries in the table.