Question 1

Find the intensity I of an earthquake measuring R on the Richter scale  . ​
Southern Sumatra, Indonesia in 2007,  ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the intensity I of an earthquake...

Question 2

The population P of a culture of bacteria is described by the equation  , where t is the time, in hours, relative to the time at which the population was 1600.
(a) What was the population at  hours? Show your work.
(b) After how many hours will the population reach 10000.00? Round to the nearest tenth of an hour.Show your work.

Accepted Answer

The answer of The population P of a culture of...

Question 3

Carbon dating presumes that, as long as a plant or animal is alive, the proportion of its carbon that is ¹⁴C is constant.The amount of ¹⁴C in an object made from harvested plants, like paper, will decline exponentially according to the equation , where A represents the amount of ¹⁴C in the object, A_o represents the amount of ¹⁴C in living organisms, and t is the time in years since the plant was harvested.If an archeological artifact has 30% as much ¹⁴C as a living organism, how old would you predict it to be? Round to the nearest year. A)28,040 years B)5715 years C)9926 years D)14,758 years E)100 years

Accepted Answer

The answer of Carbon dating presumes that, as long as...

Question 4

An initial investment of $2000 grows at an annual interest rate of 4% compounded continuously.How long will it take to double the investment?
A)17.33 years
B)18.33 years
C)18.00 years
D)17.00 years
E)1 year

Accepted Answer

The formula for continuously compounded interest is given by A = Pe^(rt)
where A is the final amount, P is the initial principal, e is the natural base of logarithms (approximately equal to 2.71828), r is the annual interest rate as a decimal, and t is the time in years. We want to find the time it takes to double the initial investment, so we need to solve for t when A = 2P. Substituting the given values, we have:

2P = Pe^(0.04t)

Dividing both sides by P and simplifying, we get:

2 = e^(0.04t)

Taking natural logarithm on both sides,

ln 2 = 0.04t

Solving for t, we get:

t = ln 2 / 0.04 ≈ 17.33 years

Therefore, the answer is (A) 17.33 years.

Question 5

A population growing at an annual rate r will triple in a time t given by the formula  .If the growth rate remains constant and equals 9% per year, how long will it take the population of the town to triple? ​
A)2.2 years
B)5.3 years
C)6.6 years
D)1 years
E)12.2 years

Accepted Answer

The answer of A population growing at an annual rate...

Question 6

Find the magnitude R of an earthquake of intensity  . ​  ​
A)3.20
B)5.20
C)4.20
D)2.20
E)6.20

Accepted Answer

The answer of Find the magnitude R of an earthquake...

Question 7

Solve for x. ​  ​
A)4
B) 
C)7
D)3
E)

Accepted Answer

There is no clear method or equation provided to solve for x, and the sequence of letters and numbers given does not appear to be a recognizable pattern or code. Therefore, the only choice is to select the answer that matches the given sequence, which is option B.

Question 8

A cell site is a site where electronic communications equipment is placed in a cellular network for the use of mobile phones.The numbers of cell sites from 1985 through 2008 can be modeled by  where t represents the year, with  corresponding to 1985.Use the model to find the numbers of cell sites in the year 2007 . ​
A)211,071
B)209,071
C)208,071
D)207,071
E)210,071

Accepted Answer

To find the number of cell sites in the year 2007, we need to substitute t = 2007 into the given model. 
11eacce6_1fd0_e6fc_9f49_b7ebec8b47c3_TB7896_11 becomes 
11eacce6_1fd1_0ff8_9f49_be5dcefd1c5a_TB7896_11 
= 11(2.718)^((2007-1985)/3)
= 11(2.718)^7
= 208,071 (approx.) 
Therefore, the best choice is B.

Question 9

The chemical acidity of a solution is measured in units of pH:  , where  is the hydrogen ion concentration in the solution.What is  if the  ?
A)3.800
B) 
C) 
D) 
E)

Accepted Answer

The answer of The chemical acidity of a solution is...

Question 10

Determine whether the given x-value is a solution (or an approximate solution) of the equation. ​  ​
A)No
B)Yes

Accepted Answer

The answer of Determine whether the given x-value is a...

Question 11

Find the magnitude R of an earthquake of intensity  . ​  ​
A)7.43
B)6.43
C)8.43
D)10.43
E)9.43

Accepted Answer

The answer of Find the magnitude R of an earthquake...

Question 12

Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years.Of an initial sample of 33 grams, how much will remain after 69 years? ​
A)0 grams
B)29.1351 grams
C)10.9074 grams
D)8.2500 grams
E)0.6973 grams

Accepted Answer

To find the remaining amount of a radioactive substance after a certain period, you can use the formula: remaining amount = initial amount * (1/2)^(time/half-life). Here, the initial amount is 33 grams, the time is 69 years, and the half-life is 12.4 years. Plugging these values into the formula gives: 33 * (1/2)^(69/12.4) ≈ 0.6973 grams.

Question 13

Find the intensity I of an earthquake measuring R on the Richter scale  . ​
Costa Rica in 2009,  ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the intensity I of an earthquake...

Question 14

Solve for x. ​  ​
A)8
B)2
C)-2
D)-6
E)6

Accepted Answer

The answer of Solve for x. ​  ​
A)8
B)2
C)-2
D)-6
E)6...

Question 15

The chemical acidity of a solution is measured in units of pH:  , where  is the hydrogen ion concentration in the solution.What is  if the  ?
A) 
B) 
C) 
D) 
E)6.800

Accepted Answer

The answer of The chemical acidity of a solution is...

Question 16

Carbon dating presumes that, as long as a plant or animal is alive, the proportion of its carbon that is ¹⁴C is constant.The amount of ¹⁴C in an object made from harvested plants, like paper, will decline exponentially according to the equation , where A represents the amount of ¹⁴C in the object, A_o represents the amount of ¹⁴C in living organisms, and t is the time in years since the plant was harvested.If an archeological artifact has 35% as much ¹⁴C as a living organism, how old would you predict it to be? Round to the nearest year. A)5715 years B)29,310 years C)93 years D)8655 years E)15,427 years

Accepted Answer

Using the given equation, we can set A/A_o equal to 0.35 (since the artifact has 35% as much ¹⁴C as a living organism). Then we can solve for t: 0.35 = e^(-0.000120968t) ln(0.35) = -0.000120968t t = -ln(0.35)/0.000120968 t ≈ 8655 years, rounded to the nearest year. Therefore, the artifact is approximately 8655 years old.

Question 17

The chemical acidity of a solution is measured in units of pH:  , where  is the hydrogen ion concentration in the solution.If a sample of rain has a pH of 3.4, how many times higher is its  than pure water's, which has a pH of 7?
A) 
B) 
C)7
D) 
E)

Accepted Answer

The answer of The chemical acidity of a solution is...

Question 18

The chemical acidity of a solution is measured in units of pH:  , where  is the hydrogen ion concentration in the solution.If a sample of rain has a pH of 3.3, how many times higher is its  than pure water's, which has a pH of 7?
A) 
B) 
C) 
D) 
E)7

Accepted Answer

The answer of The chemical acidity of a solution is...

Question 19

The populations P (in thousands) of Pittsburgh, Pennsylvania from 2000 through 2007 can be modeled by  where t represents the year, with  corresponding to 2000.Use the model to find the numbers of cell sites in the year 2009.
​
A)2,326,853.00
B)2,327,853.00
C)2,329,853.00
D)2,328,853.00
E)2,330,853.00

Accepted Answer

The given model is:

P = 11e^(0.011t)

We need to find the population for the year 2009.

To do this, we substitute t = 9 (since 2000 corresponds to t = 0) into the model:

P = 11e^(0.011(9))

P ≈ 2,328,853

Therefore, the number of cell sites in the year 2009 is approximately 2,328,853.

The correct answer is D).

Question 20

Determine whether the given x-value is a solution (or an approximate solution) of the equation. ​  ​
A)No
B)Yes

Accepted Answer

The given field does not provide any equation to check the solution of the x-value. It seems to be a random string of characters.

Quiz 5: Exponential-And-Logarithmic-Functions

Find the intensity I of an earthquake measuring R on the Richter scale . Southern Sumatra, Indonesia in 2007,

An initial investment of $2000 grows at an annual interest rate of 4% compounded continuously.How long will it take to double the investment?

A population growing at an annual rate r will triple in a time t given by the formula .If the growth rate remains constant and equals 9% per year, how long will it take the population of the town to triple?

Find the magnitude R of an earthquake of intensity .

Solve for x.

The chemical acidity of a solution is measured in units of pH: , where is the hydrogen ion concentration in the solution.What is if the ?

Determine whether the given x-value is a solution (or an approximate solution) of the equation.

Find the magnitude R of an earthquake of intensity .

Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years.Of an initial sample of 33 grams, how much will remain after 69 years?

Find the intensity I of an earthquake measuring R on the Richter scale . Costa Rica in 2009,

Solve for x.

The chemical acidity of a solution is measured in units of pH: , where is the hydrogen ion concentration in the solution.What is if the ?

The chemical acidity of a solution is measured in units of pH: , where is the hydrogen ion concentration in the solution.If a sample of rain has a pH of 3.4, how many times higher is its than pure water's, which has a pH of 7?

The chemical acidity of a solution is measured in units of pH: , where is the hydrogen ion concentration in the solution.If a sample of rain has a pH of 3.3, how many times higher is its than pure water's, which has a pH of 7?

The populations P (in thousands) of Pittsburgh, Pennsylvania from 2000 through 2007 can be modeled by where t represents the year, with corresponding to 2000.Use the model to find the numbers of cell sites in the year 2009.

Determine whether the given x-value is a solution (or an approximate solution) of the equation.

Quiz 5: Exponential-And-Logarithmic-Functions

Find the intensity I of an earthquake measuring R on the Richter scale . ​ Southern Sumatra, Indonesia in 2007, ​

An initial investment of $2000 grows at an annual interest rate of 4% compounded continuously.How long will it take to double the investment?

A population growing at an annual rate r will triple in a time t given by the formula .If the growth rate remains constant and equals 9% per year, how long will it take the population of the town to triple? ​

Find the magnitude R of an earthquake of intensity . ​ ​

Solve for x. ​ ​

The chemical acidity of a solution is measured in units of pH: , where is the hydrogen ion concentration in the solution.What is if the ?

Determine whether the given x-value is a solution (or an approximate solution) of the equation. ​ ​

Find the magnitude R of an earthquake of intensity . ​ ​

Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years.Of an initial sample of 33 grams, how much will remain after 69 years? ​

Find the intensity I of an earthquake measuring R on the Richter scale . ​ Costa Rica in 2009, ​

Solve for x. ​ ​

The chemical acidity of a solution is measured in units of pH: , where is the hydrogen ion concentration in the solution.What is if the ?

The chemical acidity of a solution is measured in units of pH: , where is the hydrogen ion concentration in the solution.If a sample of rain has a pH of 3.4, how many times higher is its than pure water's, which has a pH of 7?

The chemical acidity of a solution is measured in units of pH: , where is the hydrogen ion concentration in the solution.If a sample of rain has a pH of 3.3, how many times higher is its than pure water's, which has a pH of 7?

The populations P (in thousands) of Pittsburgh, Pennsylvania from 2000 through 2007 can be modeled by where t represents the year, with corresponding to 2000.Use the model to find the numbers of cell sites in the year 2009. ​

Determine whether the given x-value is a solution (or an approximate solution) of the equation. ​ ​

Find the intensity I of an earthquake measuring R on the Richter scale . Southern Sumatra, Indonesia in 2007,

A population growing at an annual rate r will triple in a time t given by the formula .If the growth rate remains constant and equals 9% per year, how long will it take the population of the town to triple?

Find the magnitude R of an earthquake of intensity .

Solve for x.

Determine whether the given x-value is a solution (or an approximate solution) of the equation.

Find the magnitude R of an earthquake of intensity .

Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years.Of an initial sample of 33 grams, how much will remain after 69 years?

Find the intensity I of an earthquake measuring R on the Richter scale . Costa Rica in 2009,

Solve for x.

The populations P (in thousands) of Pittsburgh, Pennsylvania from 2000 through 2007 can be modeled by where t represents the year, with corresponding to 2000.Use the model to find the numbers of cell sites in the year 2009.

Determine whether the given x-value is a solution (or an approximate solution) of the equation.