Algebra Questions
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algebraquiz.docx1.
Evaluate the function at the indicated value of x. Round your result to three decimal places.
Function: f(x) = 0.5^x Value: x = 1.7
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-0.308 |
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1.7 |
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0.308 |
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0.5 |
2.
Solve for x. 3x = 81
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7 |
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3 |
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4 |
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-3 |
3.
Logarithms are the inverse of exponentials.
True
False
4.
The Logarithm Quotient Rule states:
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logb(x / y) = logb(x) + logb(y)
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logb(x / y) = logb(x) - logb(y)
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logb(x y) = y ∙ logb(x)
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logb(c) = 1 / logc(b) |
5.
Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. Assume all variables are positive.
log3 9x
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log3 9 * log3 x |
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log3 9 - log3 |
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none of these |
6.
Select the graph of the function. Indicate which graph is correct: 1st, 2nd, 3rd, or 4th
f(x) = 5x-1
7.
Evaluate the function at the indicated value of x. Round your result to three decimal places.
Value: x=2
8.
The exponential equation y=bx is equivalent to the logarithmic equation x=logby
True
False
9.
Use the One-to-One property to solve the equation for x.
e(3x+5) = e6
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x = -1/3 |
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x2 = 6 |
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x = 1/3 |
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x = 3 |
10.
Write the logarithmic equation in exponential form.
log8 64 = 2
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82 = 16 |
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11.
Write the exponential equation in logarithmic form.
43 = 64
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log64 4 = 3 |
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12.
The given x-value is a solution (or an approximate solution) of the equation.
42x-7 = 16
x = 5
True
False
13.
Find the magnitude R of each earthquake of intensity I (let I0=1). (Hint: R=log (I/I0)
I = 19000
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5.28 |
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14.
pH is a measure of the hydrogen ion concentration of a solution. It is defined as the negative logarithm of the hydrogen ion concentration. The equation is:
pH = - log [H+]
If an acid has an H+ concentration of 10-4, what's the pH?
15.
A general formula for exponential Growth can be given by:
A = P ekt
In your textbook, or using another reliable source, research what values, P, A, k and t represent and write your answer. (Hint: What do each of the variables stand for?)
16.
Continuously compounded interest means your principal is earning interest and you keep earning interest on the interest earned. Research the formula for Continuously Compounded Interest and write it below.
17.
$2500 is invested in an account at interest rate r, compounded continuously. Find the time required for the amount to double. (Approximate the result to two decimal places.)
r = 0.0570
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13.16 years |
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10.16 years |
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18.
Write Eulers Number (e) to three decimal places.
19.
Exponential functions often involve the rate of increase or decrease of something such as a population, for example. If there is a population increase, it is a _______ function and when there is a decrease, it is a ________ function.
20.
In your post, share with us what you have found out about the number, for example, its history, some trivial facts about the number, and/or how it is applied.
21.
A system of equations:
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Has two or more equations with the same set of unknowns |
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Has one equation and two unknowns |
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Has two equations with different sets of unknowns |
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Has more sets of unknowns than equations |
22.
A system of two linear equations and two unknowns can be solved by:
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Elimination |
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Substitution |
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Graphing the equations |
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All of the above |
23.
A system of two linear equations and three unknowns can be solved by:
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Elimination |
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Substitution |
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Graphing the equations |
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It cannot be solved |
24.
A system of equations has as many equations as there are variables (unknowns).
True
False
25.
Solve these two equations by elimination, substitution or graphing
Equation 1: x+y=1
Equation 2: -2x+4y=6
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X=-1/3, y = 4/3 |
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X= 4/3, y = -1/3 |
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X=1/3, y=4/3 |
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X=-4/3, y-=1/3 |
26.
For the following System of Equations, the Matrix Form included below is correct.
2x+y+z=4
6y+5z=-33x
5y-z=27
Matrix Form:
True
False
27.
The cost C (in millions of dollars) of removing p% of the industrial and municipal pollutants discharged into a river is given by
According to this model, explain why or why not it is possible to remove 100% of the pollutants?
28.
The admission fee at the county fair is $2 for children and $4 for adults. On a certain day, 2000 people enter the fair and $5000 is collected. Using c as the variable to represent the number of children and a as the variable for adults, write a system of equations to determine how many children and how many adults attended. Note down this system of equations so that you can use it for the next question.
29.
Based on the system of equations you wrote in the previous problem, how many children attended the county fair that day?
30.
Evaluate the function ƒ(x) = 5x + 4 at ƒ(0)
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9 |
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1 |
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4 |
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0 |
31.
The profit P (in hundreds of dollars) that a company makes depends on the amount x (in hundreds of dollars) the company spends on advertising according to the model. P(x) = 230 + 40x - 0.5x2 What expenditure for advertising will yield a maximum profit?
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40 |
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0.5 |
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230 |
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20 |
32.
The concentration C (in mg/dl), of a certain antibiotic in a patient's bloodstream is given by 50t/t^2+25 where t is the time (in hours) after taking the antibiotic. What is the concentration 10 hours after taking the antibiotic?
33.
Write the logarithmic equation in exponential form.
Log2 16 = 4
34.
Find the domain of the function:
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All real numbers |
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All real numbers except x=3 |
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All positive real numbers |
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All real numbers except x=0 |
35.
pH is a measure of the hydrogen ion concentration of a solution. It is defined as the negative logarithm of the hydrogen ion concentration. The equation is:
pH = - log [H+]
If an acid has an H+ concentration of 10-7, find the pH?
36.
In order to join a movie streaming service, you pay a $75 annual fee, then $1.50 for each movie you stream. Which equation will allow you to determine the cost you will pay if you stream x number of movies? Select from the following equations and indicate the correct answer in the space below: 1st, 2nd, 3rd, or 4th.
37.
Evaluate the function at the indicated value of x.
Function: f(x) = 0.5x Value: x = 2
38.
Find the domain of the function
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Domain: all real numbers x except x=7 |
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Domain: all real numbers x |
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Domain: all real numbers x except x = -6
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39.
Express the following matrix as a system of equations:
40.
Solve for x.
4x = 16
