Question 1

The acidity of a solution is determined by the concentration H of hydrogen ions. The formula is . The accompanying exponential formula is H = 0.1^pH. Lower pH values indicate a more acidic solution. Normal rain has a pH of 5.6. Suppose acid rain has a pH of 4.3. How many times as acidic as normal rain is this? A)2 B)5 C)10 D)20

Accepted Answer

Using the formula, we can calculate the hydrogen ion concentration for normal rain and acid rain:

H(normal) = 0.1^5.6 = 2.51 x 10^-6
H(acid) = 0.1^4.3 = 5.01 x 10^-5

To determine how many times more acidic the acid rain is compared to normal rain, we need to divide the hydrogen ion concentration of acid rain by the hydrogen ion concentration of normal rain:

5.01 x 10^-5 / 2.51 x 10^-6 = 19.9

Rounding to the nearest whole number, the acid rain is approximately 20 times more acidic than normal rain. Therefore, the answer is D.

Question 2

In an area prone to earthquakes there is a 6.9 magnitude quake. Two years before there was a 6.6 magnitude quake. The relative intensity of the 6.9 quake was about twice that of the 6.6 quake.

Accepted Answer

The Richter scale is logarithmic, meaning each whole number increase on the scale represents a tenfold increase in measured amplitude and roughly 31.6 times more energy release. A 6.9 magnitude quake releases about 2 times more energy than a 6.6 magnitude quake.

Question 3

Solve the equation . 
A) 
B) 
C) 
D)

Accepted Answer

As per the question, there is no information regarding what needs to be solved for. Therefore, it is not possible to provide a definitive answer. However, the choices provided are hexadecimal numbers, and the only difference between them is the last two digits. Therefore, the best choice is the one that satisfies the given criteria. In this case, the third option, (C) 11eb6c39_79ec_7f79_8d9d_c5fcc4a60e33_TB8424_11, is the best choice as it differs from the original number by only one digit, while the other choices differ by two or more digits.

Question 4

Which of the following is a quadratic function?
A) 
B) 
C) 
D)

Accepted Answer

A quadratic function is a function with degree 2 and can be written in the form of f(x) = ax^2 + bx + c. Option B is the only one that has x^2 term, which is the characteristic of a quadratic function.

Question 5

Which of the following statements is NOT correct for the function ? 
A)The function is a quadratic function. 
B)The graph of is open downward. 
C)The vertex of the graph of is .  
D)The function has 2 distinct real zeros.

Accepted Answer

The answer of Which of the following statements is NOT...

Question 6

How many times more intense is a 6.0 magnitude earthquake than a 3.0 magnitude earthquake?
A)2
B)3
C)100
D)1000

Accepted Answer

The magnitude scale is logarithmic, meaning that each increase of 1 in magnitude represents a tenfold increase in amplitude. Therefore, a 6.0 magnitude earthquake is 1000 times more intense than a 3.0 magnitude earthquake (10x10x10=1000).

Question 7

The graph of a quadratic function has a special shape known as a:
A)line.
B)parabola.
C)hyperbola.
D)ellipse.

Accepted Answer

A quadratic function is of the form f(x) = ax^2 + bx + c where a, b, c are constants. The graph of this function is a parabola, which is a U-shaped curve. Therefore, the correct answer is B) parabola. The other options are not applicable as they correspond to different types of functions.

Question 8

Suppose that inflation is 3% per year. This means the cost of an item increases by 3% each year. Suppose a jacket cost $150 in 2011. How long will it take for the jacket to cost $200 dollars?
A)5 years
B)10 years
C)15 years
D)20 years

Accepted Answer

To find out how long it will take for the jacket to cost $200, we can use the formula for compound interest, which is also applicable for calculating inflation effects: $A = P(1 + r)^t$, where $A$ is the amount after time $t$, $P$ is the principal amount (initial amount), $r$ is the rate of increase (inflation rate), and $t$ is the time in years. Plugging in the values: $200 = 150(1 + 0.03)^t$. Solving for $t$ gives approximately 10 years.

Question 9

Radium-226 is subject to radioactive decay, and each year the amount present is reduced by 4.2%. The amount of radium-226 is an exponential function of time in years. What is the base of this exponential function?
A)0.042
B)0.238
C)0.958
D)4.2

Accepted Answer

The formula for exponential decay is given by y = ab^x, where b is the base of the exponential function. In this case, the amount of radium-226 is decreasing by 4.2% each year, so the multiplier (or decay factor) is 1 - 0.042 = 0.958. Thus, the base of the exponential function is 0.958, which corresponds to choice C.

Question 10

What is the number of distinct real solutions for the equation ? 
A)0
B)1
C)2
D)3

Accepted Answer

The answer of What is the number of distinct real...

Question 11

Suppose you make an investment of $2000 that you are not allowed to cash in for five years. Unfortunately, the value of the investment decreases by 15% per year. How long will it be before your investment decreases to half its original value?
A)2.5 years
B)3.6 years
C)4.1 years
D)4.3 years

Accepted Answer

After the first year, the investment will be worth $1700. After the second year, it will be worth $1445. After the third year, it will be worth $1228. After the fourth year, it will be worth $1044.2. After the fifth year, it will be worth $887.57. Half of the original value of $2000 is $1000. Solving for x in the equation $2000(0.85)^x = $1000 gives x approximately equal to 4.3 years. Therefore, it will take about 4.3 years for the investment to decrease to half its original value.

Question 12

A speaker is playing music at 75 decibels. A second speaker playing the same music at the same decibel reading is placed beside the first. What is the decibel reading of the pair of speakers?
A)150 decibels
B)180 decibels
C)98 decibels
D)78 decibels

Accepted Answer

When two sound sources of the same level are placed together, the total sound level only increases by about 3 decibels, in this case giving a total decibel reading of 78. Option A and B are incorrect as they involve doubling or more than doubling the sound level, which is not accurate in this scenario. Option C is also incorrect, as two sound sources of the same level do not add up to exactly the same level.

Question 13

The loudness of sound decreases as the distance from the source increases. Doubling the distance from a sound multiplies the relative intensity of the sound by one-fourth. When the sound of a speaker is recorded as 80 decibels at 10 feet, what is the decibel reading if four identical speakers are added at 20 feet?
A)83 decibels
B)84 decibels
C)92 decibels
D)93 decibels

Accepted Answer

Doubling the distance from the sound source decreases the intensity to one-fourth. For one speaker, the intensity at 20 feet would be one-fourth of that at 10 feet. Decibels (dB) are calculated on a logarithmic scale. A tenfold increase in intensity adds 10 dB, and a tenfold decrease subtracts 10 dB. Halving the intensity (which is more than a tenfold decrease) subtracts more than 10 dB, but since the intensity is one-fourth, it's effectively halving twice, which would subtract slightly more than 20 dB from the original 80 dB for one speaker. However, adding four identical speakers quadruples the intensity, which compensates for the reduction to one-fourth at double the distance, bringing the intensity back to the equivalent of one speaker at 10 feet, or 80 dB. The combined effect of these changes results in a slight increase in decibels due to the logarithmic nature of the dB scale and the addition of slightly more sound energy from the four speakers being in different locations, leading to a small increase to 83 dB.

Question 14

An increase of 1 on the pH scale causes acidity to be multiplied by a factor of 0.1, while a decrease of 1 on the pH scale causes acidity to be multiplied by a factor of 10. If pure water has a pH of 7, how many times as acidic as pure water is a solution measuring a pH of 3?
A)10
B)100
C)1000
D)10,000

Accepted Answer

Each decrease of 1 on the pH scale multiplies the acidity by a factor of 10. Therefore, a solution with a pH of 3 is 10,000 times as acidic as pure water (10 x 10 x 10 x 10 = 10,000).

Question 15

The loudness of sound decreases as the distance from the source increases. Doubling the distance from a sound multiplies the relative intensity of the sound by one-fourth. If the sound of a speaker is recorded at 80 decibels at 4 feet, what is the decibel reading at 8 feet?
A)20 decibels
B)46 decibels
C)68 decibels
D)74 decibels

Accepted Answer

Doubling the distance from a sound multiplies the relative intensity of the sound by one-fourth. So, the decibel reading at 8 feet is 80 - 6 = 74 decibels.

Question 16

An investment is growing by 9% each year. How long does it take the investment to double in value?
A)7 years
B)8 years
C)10 years
D)11 years

Accepted Answer

The Rule of 72 is a simple way to estimate the number of years required to double the investment at a given annual rate of return. By dividing 72 by the annual rate of return, investors can get a rough estimate of how many years it will take for the initial investment to duplicate itself. In this case, 72 divided by 9 equals 8 years.

Question 17

Suppose that inflation is 3% per year. This means the cost of an item increases by 3% each year. Suppose a jacket cost $150 in 2011. Find a formula that gives the cost of the jacket C in dollars after t years. A)C = $150 + 1.03^t B)C = $150 × 1.03^t C)C = $150 × 1.3^t D)C = $150 + 1.3^t

Accepted Answer

To find the cost of the jacket after t years, we need to multiply the original cost ($150) by the inflation factor (1 + 0.03)^t, which gives us $150 × 1.03^t. This is equivalent to choice B, C = $150 × 1.03^t. The other options have incorrect calculations or include an additional factor that is not necessary.

Question 18

Factor the equation . 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Factor the equation . 
A) 
B) 
C)...

Question 19

If the per capita growth rate of the world population continues to be what it was in the year 2000, the world population t years after July 1, 2000, will be 6.085 × 1.0121^t billion. According to this formula, when will the world population reach 9 billion? A)41.3 years after July 1, 2000 B)32.5 years after July 1, 2000 C)22.7 years after July 1, 2000 D)6.8 years after July 1, 2000

Accepted Answer

We are given the formula:

World population (in billions) = 6.085 × 1.0121^t

We need to find out when the world population will reach 9 billion, so we can set up the following equation:

9 = 6.085 × 1.0121^t

Divide both sides by 6.085:

1.476 = 1.0121^t

Take the natural logarithm of both sides:

ln(1.476) = ln(1.0121^t)

Using the property of logarithms that ln(a^b) = b ln(a), we can simplify the right side:

ln(1.476) = t ln(1.0121)

Finally, solve for t by dividing both sides by ln(1.0121):

t = ln(1.476) / ln(1.0121) ≈ 32.5

Therefore, the world population will reach 9 billion about 32.5 years after July 1, 2000. 
The answer is B.

Question 20

What is the product of two solutions of the equation ? 
A)-10
B)24
C)-24
D)10

Accepted Answer

The answer of What is the product of two solutions...

Quiz 3: Linear and Exponential Change: Comparing Growth Rates

In an area prone to earthquakes there is a 6.9 magnitude quake. Two years before there was a 6.6 magnitude quake. The relative intensity of the 6.9 quake was about twice that of the 6.6 quake.

Solve the equation .

Which of the following is a quadratic function?

Which of the following statements is NOT correct for the function ?

How many times more intense is a 6.0 magnitude earthquake than a 3.0 magnitude earthquake?

The graph of a quadratic function has a special shape known as a:

Suppose that inflation is 3% per year. This means the cost of an item increases by 3% each year. Suppose a jacket cost $150 in 2011. How long will it take for the jacket to cost $200 dollars?

Radium-226 is subject to radioactive decay, and each year the amount present is reduced by 4.2%. The amount of radium-226 is an exponential function of time in years. What is the base of this exponential function?

What is the number of distinct real solutions for the equation ?

Suppose you make an investment of $2000 that you are not allowed to cash in for five years. Unfortunately, the value of the investment decreases by 15% per year. How long will it be before your investment decreases to half its original value?

A speaker is playing music at 75 decibels. A second speaker playing the same music at the same decibel reading is placed beside the first. What is the decibel reading of the pair of speakers?

An increase of 1 on the pH scale causes acidity to be multiplied by a factor of 0.1, while a decrease of 1 on the pH scale causes acidity to be multiplied by a factor of 10. If pure water has a pH of 7, how many times as acidic as pure water is a solution measuring a pH of 3?

The loudness of sound decreases as the distance from the source increases. Doubling the distance from a sound multiplies the relative intensity of the sound by one-fourth. If the sound of a speaker is recorded at 80 decibels at 4 feet, what is the decibel reading at 8 feet?

An investment is growing by 9% each year. How long does it take the investment to double in value?

Suppose that inflation is 3% per year. This means the cost of an item increases by 3% each year. Suppose a jacket cost $150 in 2011. Find a formula that gives the cost of the jacket C in dollars after t years.

Factor the equation .

If the per capita growth rate of the world population continues to be what it was in the year 2000, the world population t years after July 1, 2000, will be 6.085 × 1.0121t billion. According to this formula, when will the world population reach 9 billion?

What is the product of two solutions of the equation ?

If the per capita growth rate of the world population continues to be what it was in the year 2000, the world population t years after July 1, 2000, will be 6.085 × 1.0121^t billion. According to this formula, when will the world population reach 9 billion?