Answers CR - Algebra 2 26-27 - S2Solving Logarithmic Equations using Technology

Solving Logarithmic Equations using Technology — Unit test Answers

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The two expressions below have the same value when rounded to the nearest hundredth.What is the approximate value of to the nearest hundredth?

0.93

1.23

9.16

65.53

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A biologist begins working with a sample containing 20,000 bacteria. The population size doubles every 10 days according to the equation , where t represents the number of days. After seven days the biologist begins working with a second sample of 20,000 bacteria. The equation used to represent the population of sample 2 after t days is . Which of the following is an equivalent form of the equation for the population of sample 2?

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Consider the expression . Which of the following is an equivalent expression?

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One brand of vinegar has a pH of 4.5. Another brand has a pH of 5.0. The equation for the pH of a substance is pH = –log[H+], where H+ is the concentration of hydrogen ions. What is the approximate difference in the concentration of hydrogen ions between the two brands of vinegar?

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Which is the graph of ?

On a coordinate plane, a curve starts at (2, 0) and curves up and goes through (3, 3) and (9, 5).

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On a coordinate plane, a curve starts at (2, 6) and curves down and goes through (3, 3) and (10, 2).

Jerome solved the equation below by graphing.Which of the following shows the correct system of equations and solution?

; x = 3

; x = 4

; x = 33

; x = 44

A scientist has 100 milligrams of a radioactive element. The amount of radioactive element remaining after t days can be determined using the equation . After three days, the scientist receives a second shipment of 100 milligrams of the same element. The equation used to represent the amount of shipment 2 remaining after t days is . After any time, t, the mass of the element remaining in shipment 1 is what percentage of the mass of the element remaining in shipment 2?

78.1%

81.2%

123.1%

128.0%

Two different radioactive isotopes decay to 10% of their respective original amounts. Isotope A does this in 33 days, while isotope B does this in 43 days. What is the approximate difference in the half-lives of the isotopes?

3 days

10 days

13 days

33 days

A student showed the steps below while solving the equation by graphing.Step 1:Write a system of equations: Step 2: Use the change of base formula to rewrite the equations:Step 3:Graph the two equations:Step 4:Identify the x-value at the point of intersection:In which step did the student make the first error?

step 1

step 2

step 3

step 4

Which graph shows the solution to the equation below?

On a coordinate plane, a curve starts in quadrant 3 and curves up into quadrant 1 and approaches y = 3. It crosses the x-axis at (1, 0). A horizontal straight line is at y = 1.

On a coordinate plane, a curves starts in quadrant 4 and curves up into quadrant 1 and approaches y = 3. It crosses the x-axis at (1, 0). A horizontal straight line is at y = negative 1.

On a coordinate plane, a curve starts in quadrant 3 and curves up into quadrant 1 and approaches y = 1. It crosses the x-axis at (negative 1, 0). A horizontal straight line is at y = 1.

On a coordinate plane, a curves starts in quadrant 3 and curves up into quadrant 1 and approaches y = 2. It crosses the x-axis at (negative 1, 0). A horizontal straight line is at y = negative 1.

What are the domain and range of ?

domain: x > 1; range: y > 2

domain: x > 1; range: all real numbers

domain: all real numbers; range: y > 1

domain: all real numbers; range: all real numbers

Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10%. The second car depreciates at an annual rate of 15%. What is the approximate difference in the ages of the two cars?

1.7 years

2.0 years

3.1 years

5.0 years

Which of the following shows the graph of y = –(2)x – 1?

On a coordinate plane, a curve is level at y = 0 in quadrant 2 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, negative 0.5).

On a coordinate plane, a curve is level at y = negative 1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, negative 2).