### A logarithm as an exponent is justified.

A logarithm is an exponent. Explain, in your own words, why this is so. Justify your explanation with an example.

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A logarithm is an exponent. Explain, in your own words, why this is so. Justify your explanation with an example.

Identify the important characteristics of an exponential function. Explain the difference between the graph of an exponential growth function and an exponential decay function and give an example of each type of function.

1) A man has a simple discount note for $6,300 at an ordinary bank discount rate of 8.72%, for 60 days. What is the effective interest rate? Round to the nearest tenth of a percent. Use the bankers rule. 2) Find the discount and proceeds on a 3,240 face value note for six months if the discount rate is 9.3%. Round to the near

I am submitting a complex set of data points that I would like someone to use, employing LaGrange Interpolation (or any other process that might be more appropriate), to give me another detailed example to use as I try to learn the process and employ it to other problems. The points are: (0,214), (0.11,2022), (0.65,1131), (1

Typing hint: Type x2 as x^2 (shift 6 on the keyboard will give ^) 1) Solve the following quadratic equation by factoring: a) x2 â?' 6x â?'16 = 0 Answers: Show your work here: b) Solve the quadratic equation 6x2 + 3x â?" 18 = 0 using the quadratic formula. Read the information in the assignment list to learn more a

Four different methods of solving a quadratic equation have been discussed: factoring, the square root property, completing the square, and the quadratic formula. Explain under what circumstances each method would be preferred over any of the other methods. Give an example for each circumstance.

What is the square root property and what is it used for? In what form should an equation be, in order to use the square root property? When should the square root property be used instead of factoring?

Let F be a field and let K be an algebraically closed field with F â?? K. If f â??F[x] is irreducible (i.e. if f = m * n , then one of m or n is a constant) and f has a multiple zero in K , then f â?² = 0

line passes through the point (5,1) and has a slope of 2 write an equation for this line find the equation for the line 1,-5 and -4,3 find the equation for the line -2,-1 and -3,4 write equations for the horizontal and vertical lines passing through point (-1,9) consider the line -8x-2y=-5 what is the slope of the

I am having difficulties with two practice word problems attached. Please help. Word Problems: 1. The octane rating of a gasoline is a measure of the amount of isooctane in the gas. Subaru recommends 91-octane gasoline for the 2008 Legacy 3.0 R. How much 87-octane gas and 93-octane gas should Kelsey mix in order to make 12 g

Take the current amount you have in your checking or savings account. Suppose you have a choice of keeping your money for five years in a savings account with a 2% interest rate, or in a five year certificate of deposit with and interest rate of 4.5%. Calculate how much interest you would earn with each option over five years

What is the difference between radical equation and rational exponents?

In 2000, the average cost of tuition and fees at public four- year colleges was $3500, and in 2005 it was $5100. The supporting information is listed below. Note that the known value for 2001 is $3700. 1.) Cost of Tuition Plot (00,162) and (5,201) to see the shape of the line Slope= (201-162)/5 = 7.8

Show how to calculate distance and time using rational exponents and radial equations.

Year 1996 1998 2000 2002 Percentage 28 36 43 51 Draw a scatter plot and find the equation of the lest square line for the given data. From the least square equation, find the percentage for year 1999.

Use Y=196x-379,400 to estimate the number of radio stations on the air in 1975 and 1985. X(Year) 1950 1960 1970 Y(Stations) 2800 4100 6800 X(Year) 1980 1990 2000 Y(Stations) 8600 10,800 12,600 What are the steps asociated with completing this problem?

A boat is cruising at a constant speed of 20 ft/sec along a course that is parallel to a straight shoreline and 100 ft from it. A spectator standing on the shore begins to videotape the boat as soon as it passes him. (See the attached diagram.) Find the rate at which the spectator must rotate his camera in order to keep the boat

The following table represents weekly sales of a product (in $1,000s). Week Sales 1 14 2 13 3 17 4 14 Forecast sales for week 5 using exponential smoothing with a smoothing constant of 0.4 . Assume the forecast for week 1 is perfect.

In an exponential smoothing model, if the smoothing constant (alpha) were equal to 0, then a. the forecast would never change. b. the forecast would be the same as the forecast for the naive model. c. the MAD would always equal 0. d. the forecast would be impossible to calculate.

In your own words, explain the process of factoring a trinomial with a leading coefficient that is not equal to one. Why is this process more difficult than when the leading coefficient is equal to one? Give an example.

1) I am trying to solve the following quadratic equations that I have been studying for a test. a) x^2+7x+10=0 b) 2x^2-3x-2=0 2) Compute the discriminant of the quadratic equation 3x^2+x+2=0, then write a brief sentence describing the number and type of solutions for this equation.

1. Solve the following quadratic equation by factoring. a) x^2 + 7x + 10 = 0 b) 2x^2 - 3x - 2 = 0 2. Compute the discriminant of the quadratic equation 3x^2+x+2=0. Briefly describe the number and type of solutions for this equation.

1. Construct a truth table for (p Λ q) → ~p. Be sure to include all intermediate steps in the table. 3. Construct a truth table for p ↔ (q V ~ p). Include all intermediate steps in the table. 4. Given p is true, q is true, and r is false, find the truth value of the statement ~q → (p V r). 5. Wr

What constitutes a rational expression? Please give an example for reference. How would you explain this concept to someone unfamiliar with it?

What are like terms? Explain how the distributive property is used to combine like terms.

How can I factor the following polynomials? What is the best way to go about it? 1. 3x3 â?" 3x2â?" 3xâ?" 2x2 + 5 2. 9x4y3 + 18x3y2 + 18 x3y â?" 4x2y3 + 36x2 â?" 8xyâ?" 8xy2 â?" 16 3. 25y2x2 â?" 81z2

(1) Factor the following polynomial. Please describe every step: x4 + 6x3 7x2 32x 144 (2) Make a plot of the function f(x) = x4 + 6x3 7x2 32x 150 for values of x between -5 and 5 Can you comment on the roots of this function?

Antonio is a simple minded carpenter. He bought a shipment of external drywall panels (12 ft x 4 ft) that he wants to use for building new houses in a new development. He does not want to cut them, which means his houses will have a precise relationships between height, width, and depth. Zoning regulations require that homes sho

1. When simplifying like terms, how do you determine the like terms? 2. How do you determine the common factors in an expression? 3. What is factoring by grouping? When factoring a trinomial by grouping, why is it necessary to write the trinomial in four terms? 4. What is a common factor? Where do you use the common fac

Given, this partial equation, how do I complete it? Finding the width I used this equation - L= 2W + 2 I know my length is 10 feet. 10 = 2W + 2 10 -2 ft = 2W +2 - 2 8 = 2W 8/2 = 2W/2