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100
Use transformations of the graph f(x)=2x to identify the graph of the function given below. Use the graph to determine its domain, range, and asymptote.
Identify the graph of g=2x-2
What is the domain?
What is the range?
What is the asymptote?
The graph is D.
(-∞,∞)
(-2,∞)
-2
(-∞,∞)
(-2,∞)
-2
100
Write the following equation in its equivalent exponential form. log5125=y
5y=125
100
Evaluate the expression without using a calculator. log81/8
-1
100
Evaluate the following expression without using a calculator. log55
1
100
Evaluate the expressing without using a calculator. log71
0
200
Use transformations of the graph of f(x)=ex to identify the graph of the function given below. Use the graph to determine its domain, range, and asymptote.
Identify the graph of g(x)=ex-4
What is the domain?
What is the range?
What is the asymptote?
The graph is A.
(-∞,∞)
(-4,∞)
-4
(-∞,∞)
(-4,∞)
-4
200
Write the following equation in its equivalent logarithmic form. 93=x
3=log9x
200
Write the following equation in its equivalent logarithmic form. 93=x
3=log9x
200
Evaluate the expression without using a calculator. log337
7
200
Find the exact value of the logarithm without using a calculator. log525
2
300
Evaluate the expression without using a calculator.
10log36
36
300
Evaluate the expression without using a calculator. ln e6
6
300
Evaluate the expression without using a calculator.
ln e3x
3x
300
Use properties of logarithms to expand the logarithmic expression as much as possible. evaluate logarithmic expressions without using a calculator if possible.
logb (x3y/z3)
3logbx+logby-3logbz
300
Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expression.
2ln(9x)=6
What is the exact solution?
What is the decimal approximation to the solution?
e3/9
2.23
2.23
400
The graph is C.
4
(4,∞)
<-∞,∞)
4
(4,∞)
<-∞,∞)
400
Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expression. Give the exact answer.
log2(5x+3)=4
13/5
400
Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer.
log3(x+4)-log3(x-4)=2
What is the solution set?
The solution set is 5.
400
Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. give the exact answer.
ln(x-5)+ln(x+2)=ln(x-14)
What is the solution set?
There is no solution.
400
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer.
log54+log5x=1
5/4
500
Use the compund interest formulas A=P(1+r/n)nt and A=Pert to solve the problem given. Round answers to the nearest cent.
Find the accumulated value of an investment of $25,000 for 5 years at an interest rate of 5% if the money is a. compounded semiannually; b. compounded quarterly; c. compound monthly d. compounded continuously.
23,002.11
32,050.93
32,083.97
32,100.64
32,050.93
32,083.97
32,100.64
500
Solve the exponential equation. Express the solution set in terms of natural logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution.
e7x-2-5=15,890
What is the solution in terms of natural logarithms?
What is the decimal approximation for the solution?
ln 15,895+2/7
1.67
1.67
500
The formula A=23.1e0.0152t models the population of a US state, A, in millions, t years after 2000.
What was the population of the state in 2000?
When will the population of the state reach 28.3 million?
23.1
2013
2013
500
The function A=A0e-0.007770x Models the amount in pounds a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 400 pounds of the material are initially put into the vault, how many pounds will be left after 170 years? Round to the nearest whole number.
108 pounds.
500
The function A=A0e-0.01386x models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 500 pounds of the material are placed in the vault, how much time will need to pass for only 82 pounds to remain? Round to the nearest whole number.
130 years.