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.

Graph by hand f(x)= -2tan(x/2) for x between 0 and 2pi. Show a table of values.

The population P of Buffalo, New York, from 1980 to 2018 can be approximated by the function P(t)= 356,656(0.991)t  where t represents the number of years since 1980. Interpret the meaning of the base of the function.

The table gives two functions of the form P (t) = a b' that represent the populations of a Central American country and a Northern European country, t years after a baseline census is taken. Part: 0/3 Part 1 of 3 (a) For each function given in the table, write an equivalent function using base e. That is, write a function of the form P (t)=Poet. Also, determine the population of each country in the baseline census. Round the value of k to five decimal places. Country P(t)=ab' Central American P(t)=4.3 (1.0135) Northern European P(t)=4.6 (1.0062) P(t)=Poekt P(t) = P(t) = Baseline Population (in millions) P(0) - P(0) =

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%?

Evaluate the function f(x) at the given numbers (correct to six decimal places). x² - 8x f(x) f(8.5) f(8.1) f(8.05) = f(8.01) = f(8.005) = f(8.001) = f(7.9) f(7.95) = f(7.99) = f(7.995) = f(7.999) = = = = = lim X-8 x²- x². - X- - x - 56 Guess the value of the limit of f(x) as x approaches 8, correct to six decimal places. (If an answer does not exist, enter DNE.) x28x 56 = x = 8.5, 8.1, 8.05, 8.01, 8.005, 8.001, 7.9, 7.95, 7.99, 7.995, 7.999 1

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."

The population of a herd of deer is represented by the function A(t) = 205(1.16)*, where t is given in years. To the nearest whole number, what will the herd population be after 9 years? (Round your answer up to the nearest whole number.) deer

Which is larger, f(0) or g(0)?