Deck 3: Exponential and Logarithmic Functions

Question 1

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 $A = A _ { 0 } e ^ { - 0.0001213 t }$ , 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

Answer 1

8655 years

Question 2

The value V (in millions of dollars) of a famous painting can be modeled by $V = 10 e ^ { i t }$ where t represents the year, with t = 0 corresponding to 2000.In 2008, the same painting was sold for $65 million.Predict the value of the painting in 2018.(Round your answer to two decimal places.)

A)$674.61 million
B)$874.61 million
C)$474.61 million
D)$774.61 million
E)$574.61 million

Answer 2

$674.61 million

Question 3

The population P (in thousands) of Orlando, Florida from 2000 through 2007 can be modeled by $P = 1530.6 e ^ { k t }$ where t represents the year, with $t = 0$ corresponding to 2000.In 2006, the population of Orlando, Florida was about 1,883,000.00.Find the value of k.

A)k = 0.03183
B)k = 0.02863
C)k = 0.02163
D)k = 0.03453
E)k = 0.03063

Answer 3

k = 0.03453

Question 4

Select the correct graph for the given function $y = 7 e ^ { - x / 4 }$

A)
B)
C)
D)
E)

Question 5

Find the exponential model $y = a e ^ { 0.7675 x }$ that fits the points shown in the graph.

A) $y = e ^ { - 0.7675 x }$
B) $y = e ^ { 0.7675 x }$
C) $y = - e ^ { - 0.7675 x }$
D) $y = x e ^ { 0.7675 }$
E) $y = - x e ^ { - 0.7675 }$

Question 6

Select the correct graph for the given function $y = 5 e ^ { - ( x - 2 ) ^ { 2 } / 5 }$

A)
B)
C)
D)
E)

Question 7

Select the correct graph for the given function $y = \frac { 6 } { 1 + e ^ { - 2 x } }$

A)
B)
C)
D)
E)

Question 8

Select a scatter plot of the given data. $\begin{array}{|c|c|c|c|c|c|c|}\hline r & 7 \% & 8 \% & 11 \% & 12 \% & 14 \% & 15 \% \\\hline t & 16.24 & 14.27 & 10.53 & 9.69 & 8.38 & 7.86 \\\hline\end{array}$

A)
B)
C)
D)
E)

Question 9

The populations P (in thousands) of Pittsburgh, Pennsylvania from 2000 through 2007 can be modeled by $P = \frac { 2632 } { 1 + 0.083 e ^ { 0.0500 t } }$ where t represents the year, with $t = 0$ 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

Question 10

An initial investment of $5000 doubles in value in 6.3 years.Assuming continuous compounding, what was the interest rate? Round to the nearest tenth of a percent.

A)11.0%
B)4.8%
C)5.5%
D)6.3%
E)100%

Question 11

Select the correct graph for the given function $y = \ln ( x + 2 )$

A)
B)
C)
D)
E)

Question 12

The population P of a bacteria culture is modeled by $P = 4100 e ^ { k t }$ , where t is the time in hours.If the population of the culture was 5800 after 40 hours, how long does it take for the population to double? Round to the nearest tenth of an hour.

A)54.8 hours
B)8.9 hours
C)79.9 hours
D)81.7 hours
E)56.6 hours

Question 13

The population P (in thousands) of Reno, Nevada from 2000 through 2007 can be modeled by $P = 346.8 e ^ { k t }$ where t represents the year, with $t = 0$ corresponding to 2000.In 2005, the population of Reno was about 395,000.According to the model, during what year will the population reach 486,000.00?

A)2013
B)2005
C)2021
D)2017
E)2009

Question 14

An initial investment of $4000 grows at an annual interest rate of 5% compounded continuously.How long will it take to double the investment?

A)1 year
B)14.40 years
C)13.86 years
D)14.86 years
E)13.40 years

Question 15

If $1 is invested in an account over a 10-year period, the amount in the account, where t represents the time in years, is given by $A = 1 + 0.075 \| t \mid \| \text { or } A = e ^ { 0.07 t }$ depending on whether the account pays simple interest at $7 \frac { 1 } { 2 } \%$ or continuous compound interest at 7%.Graph each function on the same set of axes.Which grows at a higher rate?

A)
B)
C)
D)
E)

Question 16

Select the correct graph for the given function $y = 4 e ^ { x / 2 }$

A)
B)
C)
D)
E)

Question 17

Select the correct graph for the given function
$y = 5 + \log ( x + 2 )$

A)
B)
C)
D)
E)

Question 18

Find the exponential model $y = a e ^ { 0.5756 x }$ that fits the points shown in the graph.

A) $y = \frac { 1 } { 2 } e ^ { - 0.5756 x }$
B) $y = - \frac { 1 } { 2 } x e ^ { - 0.5756 }$
C) $y = \frac { 1 } { 2 } x e ^ { 0.5756 }$
D) $y = \frac { 1 } { 2 } e ^ { 0.5756 x }$
E) $y = - \frac { 1 } { 2 } e ^ { - 0.5756 x }$

Question 19

The population P of a culture of bacteria is described by the equation $P = 1300 e ^ { 0.052 t }$ , where t is the time, in hours, relative to the time at which the population was 1300.What was the population at $t = 3$ hours?

A) $P ( 3 ) \approx 1419$
B) $P ( 3 ) \approx 1519$
C) $P ( 3 ) \approx 1319$
D) $P ( 3 ) \approx 1619$
E) $P ( 3 ) \approx 1719$

Question 20

The number y of hits a new search-engine website receives each month can be modeled by $y = 4080 e ^ { k t }$ where t represents the number of months the website has been operating.In the website's third month, there were 10,000 hits.Find the value of k, and use this value to predict the number of hits the website will receive after 22 months.

A) $k = 0.2988$ ; About 184,894,691,979 hits
B) $k = 0.2988$ ; About 2,921,047 hits
C) $k = 0.2988$ ; About 22,832,533,585 hits
D) $k = 0.2988$ ; About 57,970,933 hits
E) $k = 0.2988$ ; About 1,150,488,266 hits

Question 21

Find the intensity I of an earthquake measuring R on the Richter scale $\left( \text { let } I _ { 0 } = 1 \right)$ .
Southern Sumatra, Indonesia in 2007, $R = 8.25$

A) $10 ^ { 8.25 } \approx 177,822,941$
B) $10 ^ { 8.25 } \approx 177,827,941$
C) $10 ^ { 8.25 } \approx 177,825,941$
D) $10 ^ { 8.25 } \approx 177,832,941$
E) $10 ^ { 8.25 } \approx 177,829,941$

Question 22

Find the magnitude R of an earthquake of intensity $I \left( \text { let } I _ { 0 } = 1 \right. \text { ) }$ . $I = 16000$

A)3.20
B)5.20
C)4.20
D)2.20
E)6.20

Question 23

Determine whether the given x-value is a solution (or an approximate solution) of the equation. $\begin{array} { l } 4 ^ { 3 x - 10 } = 16 \\x = 4\end{array}$

Question 24

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

Question 25

Solve for x. $6 ^ { x } = 36$

A)8
B)2
C)-2
D)-6
E)6

Question 26

The chemical acidity of a solution is measured in units of pH: $\mathrm { pH } = - \log \left[ \mathrm { H } ^ { + } \right]$ , where $\left[ \mathrm { H } ^ { + } \right]$ is the hydrogen ion concentration in the solution.What is $\left[ \mathrm { H } ^ { + } \right]$ if the $\mathrm { pH } = 3.8$

A)3.800
B) $6.31 \times 10 ^ { - 4 }$
C) $6.31 \times 10 ^ { - 3 }$
D) $1.58 \times 10 ^ { - 3 }$
E) $1.58 \times 10 ^ { - 4 }$

Question 27

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

Question 28

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 $y = \frac { 237,101 } { 1 + 1950 e ^ { - 0.355 t } }$ where t represents the year, with $t = 5$ 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

Question 29

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 $A = A _ { 0 } e ^ { - 0.0001213 t }$ , 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

Question 30

Determine whether the given x-value is a solution (or an approximate solution) of the equation. $\begin{array} { l } 4 ^ { 5 x - 5 } = 256 \\x = 2\end{array}$

Question 31

The chemical acidity of a solution is measured in units of pH: $\mathrm { pH } = - \log \left[ \mathrm { H } ^ { + } \right]$ , where $\left[ \mathrm { H } ^ { + } \right]$ is the hydrogen ion concentration in the solution.What is $\left[ \mathrm { H } ^ { + } \right]$ if the $\mathrm { pH } = 6.8$ ?

A) $1.58 \times 10 ^ { - 7 }$
B) $6.31 \times 10 ^ { - 7 }$
C) $6.31 \times 10 ^ { - 6 }$
D) $1.58 \times 10 ^ { - 6 }$
E)6.800

Question 32

The chemical acidity of a solution is measured in units of pH: $\mathrm { pH } = - \log \left[ \mathrm { H } ^ { + } \right]$ , where $\left[ \mathrm { H } ^ { + } \right]$ 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 $\left[ \mathrm { H } ^ { + } \right]$ than pure water's, which has a pH of 7?

A) $5.0 \times 10 ^ { 4 }$
B) $2.0 \times 10 ^ { 4 }$
C) $2.0 \times 10 ^ { 3 }$
D) $5.0 \times 10 ^ { 3 }$
E)7

Question 33

Find the magnitude R of an earthquake of intensity $\left. I \text { (let } I _ { 0 } = 1 \right)$ . $I = 270300000$

A)7.43
B)6.43
C)8.43
D)10.43
E)9.43

Question 34

Solve for x.Approximate the result to three decimal places. $e ^ { x } = 4$

A) $\ln 4 \approx 1.466$
B) $\ln 4 \approx 1.476$
C) $\ln 4 \approx 1.436$
D) $\ln 4 \approx 1.386$
E) $\ln 4 \approx 1.456$

Question 35

Solve for x. $\ln x - \ln 5 = 0$

A) $- \frac { 1 } { 5 }$
B) $- 5$
C) $\frac { 1 } { 5 }$
D) $5 ^ { - 2 }$
E)5

Question 36

Solve for x. $\left( \frac { 1 } { 4 } \right) ^ { x } = 64$

A)4
B) $- 3$
C)7
D)3
E) $- 4$

Question 37

Find the intensity I of an earthquake measuring R on the Richter scale $\text { (let } I _ { 0 } = 1 \text { ) }$ .
Costa Rica in 2009, $R = 5.70$

A) $10 ^ { 5.70 } \approx 503,187$
B) $10 ^ { 5.70 } \approx 501,187$
C) $10 ^ { 5.70 } \approx 506,187$
D) $10 ^ { 5.70 } \approx 496,187$
E) $10 ^ { 5.70 } \approx 499,187$

Question 38

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.

Question 39

A population growing at an annual rate r will triple in a time t given by the formula $t = \frac { \ln 3 } { r }$ .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

Question 40

The chemical acidity of a solution is measured in units of pH: $\mathrm { pH } = - \log \left[ \mathrm { H } ^ { + } \right]$ , where $\left[ \mathrm { H } ^ { + } \right]$ 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 $\left[ \mathrm { H } ^ { + } \right]$ than pure water's, which has a pH of 7?

A) $4.0 \times 10 ^ { 3 }$
B) $2.5 \times 10 ^ { 4 }$
C)7
D) $2.5 \times 10 ^ { 3 }$
E) $4.0 \times 10 ^ { 4 }$

Question 41

Solve the exponential equation algebraically.Approximate the result to three decimal places. $3 e ^ { x } = 15$

A) $\ln 5 \approx - 1.609$
B) $\ln 5 \approx 1.099$
C) $\ln 5 \approx - 1.099$
D) $\ln 5 \approx 1.609$
E) $\ln 5 \approx 2.708$

Question 42

Solve the exponential equation algebraically.Approximate the result to three decimal places. $2 \left( 5 ^ { 2 - x } \right) = 12$

A) $2 - \frac { \ln 6 } { \ln 5 } \approx 3.887$
B) $2 - \frac { \ln 6 } { \ln 5 } \approx 1.887$
C) $2 - \frac { \ln 6 } { \ln 5 } \approx 0.887$
D) $2 - \frac { \ln 6 } { \ln 5 } \approx 4.887$
E) $2 - \frac { \ln 6 } { \ln 5 } \approx 2.887$

Question 43

Solve for x. $\log x = - 4$

A) $- 4$
B)0.0001
C) $- 0.0001$
D) $4$
E)1.386

Question 44

Solve the exponential equation algebraically.Approximate the result to three decimal places. $4 \left( 5 ^ { x - 5 } \right) = 24$

A) $5 + \frac { \ln 6 } { \ln 5 } \approx 7.113$
B) $5 + \frac { \ln 6 } { \ln 5 } \approx 9.113$
C) $5 + \frac { \ln 6 } { \ln 5 } \approx 6.113$
D) $5 + \frac { \ln 6 } { \ln 5 } \approx 8.113$
E) $5 + \frac { \ln 6 } { \ln 5 } \approx 10.113$

Question 45

Solve for x.Approximate the result to three decimal places. $\log _ { 7 } x = \frac { 1 } { 2 }$

A) $\sqrt { 7 } \approx 2.828$
B) $\sqrt { 7 } = 2.646$
C) $\sqrt { 7 } \approx - 2.646$
D) $\sqrt { 7 } \approx 2.646$
E) $\frac { \sqrt { 7 } } { 7 } \approx 2.646$

Question 46

Solve the exponential equation algebraically.Approximate the result to three decimal places. $2 ^ { x - 5 } = 16$

A)10
B)11
C)9
D)-9
E)12

Question 47

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { x } = e ^ { x ^ { 2 } - 12 }$

A) $3 , - 4$
B) $- 3 , - 4$
C) $3,4$
D) $- 3,4$
E) $- 3,3$

Question 48

Solve the exponential equation algebraically.Approximate the result to three decimal places. $1000 e ^ { - 4 x } = 75$

A) $- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx 2.648$
B) $- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx - 1.352$
C) $- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx 1.648$
D) $- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx 0.648$
E) $- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx - 0.352$

Question 49

Solve the exponential equation algebraically.Approximate the result to three decimal places.
$e ^ { 2 x } - 7 e ^ { x } - 8 = 0$

A) $\ln 8 \approx 3.079$
B) $\ln 8 \approx 2.079$
C) $\ln 8 \approx 4.079$
D) $\ln 8 \approx 1.079$
E) $\ln 8 \approx 0.079$

Question 50

Solve for x.Approximate the result to three decimal places. $\ln x = - 2$

A) $e ^ { - 2 } \approx 7.389$
B) $e ^ { - 2 } \approx 0.368$
C) $e ^ { - 2 } \approx 2.718$
D) $e ^ { - 2 } \approx 0.135$
E) $e ^ { - 2 } \approx 1.000$

Question 51

Solve the exponential equation algebraically.Approximate the result to three decimal places. $6 ^ { - 5 x } = 0.50$

A) $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.072$
B) $\frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.517$
C) $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.387$
D) $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx 0.077$
E) $- \frac { \ln ( 0.50 ) } { 5 \ln 6 } \approx - 0.077$

Question 52

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { - 4 x ^ { 2 } } = e ^ { 3 x ^ { 2 } - 14 x }$

A) $4,2$
B) $3,2$
C) $- 4,2$
D) $0,2$
E) $0 , - 2$

Question 53

Solve the exponential equation algebraically.Approximate the result to three decimal places. $6 ^ { x } + 8 = 57$

A) $\frac { \ln 49 } { \ln 6 } \approx 2.172$
B) $\frac { \ln 49 } { \ln 6 } \approx - 0.460$
C) $\frac { \ln 49 } { \ln 6 } \approx 0.514$
D) $\frac { \ln 49 } { \ln 6 } \approx 0.460$
E) $\frac { \ln 49 } { \ln 6 } \approx - 2.172$

Question 54

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { x } - 6 = 13$

A) $\ln 19 \approx - 2.565$
B) $\ln 19 \approx 2.944$
C) $\ln 19 \approx 1.792$
D) $\ln 19 \approx 2.565$
E) $\ln 19 \approx - 2.944$

Question 55

Solve the exponential equation algebraically.Approximate the result to three decimal places.
$- 22 + 4 e ^ { x } = 13$

A) $\ln \frac { 35 } { 4 } \approx 1.169$
B) $\ln \frac { 35 } { 4 } \approx 4.169$
C) $\ln \frac { 35 } { 4 } \approx 2.169$
D) $\ln \frac { 35 } { 4 } \approx 0.169$
E) $\ln \frac { 35 } { 4 } \approx 3.169$

Question 56

Solve the exponential equation algebraically.Approximate the result to three decimal places. $4 e ^ { x } = 33$

A) $\ln \frac { 33 } { 4 } \approx 2.110$
B) $\ln \frac { 33 } { 4 } \approx - 2.110$
C) $\ln \frac { 4 } { 33 } \approx 2.110$
D) $\ln \frac { 33 } { 4 } \approx 3.497$
E) $\ln \frac { 33 } { 4 } \approx 0.114$

Question 57

Solve the exponential equation algebraically.Approximate the result to three decimal places. $2 \left( 3 ^ { x } \right) = 36$

A) $\frac { \ln 18 } { \ln 3 } \approx 0.380$
B) $\frac { \ln 18 } { \ln 3 } \approx - 0.380$
C) $\frac { \ln 18 } { \ln 3 } \approx - 2.631$
D) $\frac { \ln 3 } { \ln 18 } \approx 2.631$
E) $\frac { \ln 18 } { \ln 3 } \approx 2.631$

Question 58

Solve the exponential equation algebraically.Approximate the result to three decimal places. $3 ^ { 8 x } = 2400$

A) $\frac { \ln 2400 } { 8 \ln 3 } \approx 0.018$
B) $\frac { \ln 2400 } { 8 \ln 3 } \approx 0.886$
C) $\frac { \ln 2400 } { 8 \ln 3 } \approx 0.089$
D) $\frac { \ln 2400 } { 8 \ln 3 } \approx - 0.886$
E) $\frac { \ln 2400 } { 8 \ln 3 } \approx 1.248$

Question 59

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { 3 x } = 75$

A) $\frac { \ln 75 } { 3 } \approx 0.439$
B) $\frac { \ln 75 } { 3 } \approx 2.439$
C) $\frac { \ln 75 } { 3 } \approx - 0.561$
D) $\frac { \ln 75 } { 3 } \approx 3.439$
E) $\frac { \ln 75 } { 3 } \approx 1.439$

Question 60

Solve the exponential equation algebraically.Approximate the result to three decimal places. $e ^ { x } = e ^ { x ^ { 2 } - 30 }$

A) $- 6 , - 5$
B) $1 , - 30$
C) $6,5$
D) $- 6,5$
E) $6 , - 5$

Question 61

$3000 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to triple.(Approximate the result to two decimal places.) $r = 0.03$

A)37.62 yr
B)36.62 yr
C)35.62 yr
D)34.62 yr
E)38.62 yr

Question 62

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $8 + 71 \ln x = 14$

A) $e ^ { 6 / 7 } \approx 3.356$
B) $e ^ { 6 / 7 } \approx 1.356$
C) $e ^ { 6 / 7 } \approx 4.356$
D) $e ^ { 6 / 7 } \approx 2.356$
E) $e ^ { 6 / 7 } \approx 0.356$

Question 63

Solve $\left( \frac { 1 } { 4 } \right) ^ { x } = 64$ for x.

A)-3
B)-4
C)-1
D)1
E)no solution

Question 64

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $6 \ln x = 5$

A) $e ^ { 5 / 6 } \approx 0.301$
B) $e ^ { 5 / 6 } \approx 1.301$
C) $e ^ { 5 / 6 } \approx 3.301$
D) $e ^ { 5 / 6 } \approx 2.301$
E) $e ^ { 5 / 6 } \approx 4.301$

Question 65

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $2 \log _ { 3 } ( 0.5 x ) = 5$

A) $2 \left( 3 ^ { 5 / 2 } \right) \approx 33.177$
B) $2 \left( 3 ^ { 5 / 2 } \right) \approx 30.177$
C) $2 \left( 3 ^ { 5 / 2 } \right) \approx 31.177$
D) $2 \left( 3 ^ { 5 / 2 } \right) \approx 29.177$
E) $2 \left( 3 ^ { 5 / 2 } \right) \approx 32.177$

Question 66

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\ln 2 x = 3$

A) $\frac { e ^ { 3 } } { 2 } \approx 8.043$
B) $\frac { e ^ { 3 } } { 2 } \approx 10.043$
C) $\frac { e ^ { 3 } } { 2 } \approx 12.043$
D) $\frac { e ^ { 3 } } { 2 } \approx 11.043$
E) $\frac { e ^ { 3 } } { 2 } \approx 13.043$

Question 67

Solve for x: $7 \left( 10 ^ { x - 3 } \right) = 23$ .Round to 3 decimal places.

A)0.517
B)no solution
C)3.517
D)-1.362
E)1.362

Question 68

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\log x = 4$

A)1,000
B)1,000,000
C)10,000
D)100,000
E)100

Question 69

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\ln x = - 5$

A) $e ^ { - 5 } \approx 2.007$
B) $e ^ { - 5 } \approx 1.007$
C) $e ^ { - 5 } \approx 3.007$
D) $e ^ { - 5 } \approx - 1.993$
E) $e ^ { - 5 } \approx 0.007$

Question 70

Solve for x: $5 ^ { - x / 3 } = 0.0052$ .Round to 3 decimal places.

A)-20.606
B)9.803
C)20.606
D)-3.268
E)15.777

Question 71

Determine whether or not $x = \frac { 3 } { 7 }$ is a solution to $3 ^ { 3 x - 3 } = 81$ .

Question 72

$4500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to triple.(Approximate the result to two decimal places.) $r = 0.0315$

A)21.00 yr
B)20.00 yr
C)34.88 yr
D)24.00 yr
E)23.00 yr

Question 73

Solve the equation algebraically.Round the result to three decimal places. $\frac { 3 + \ln x } { 8 } = 0$

A) $e ^ { - 3 } \approx 2,980.958$
B) $e ^ { - 3 } \approx 0$
C) $e ^ { - 3 } \approx 54.598$
D) $e ^ { - 3 } \approx 0.050$
E) $e ^ { - 3 } \approx 20.086$

Question 74

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\log _ { 5 } ( 5 x - 3 ) = \log _ { 5 } ( 4 x + 4 )$

A)8
B)6
C)-1
D)7
E)9

Question 75

$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.) $r = 0.06$

A)13.55 yr
B)10.55 yr
C)12.55 yr
D)9.55 yr
E)11.55 yr

Question 76

$5500 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.) $r = 0.0540$

A)13.84 yr
B)10.84 yr
C)12.84 yr
D)11.84 yr
E)14.84 yr

Question 77

Solve the exponential equation algebraically.Approximate the result to three decimal places.
$e ^ { 2 x } - 7 e ^ { x } - 8 = 0$

A) $\ln 8 \approx 3.079$
B) $\ln 8 \approx 1.079$
C) $\ln 8 \approx 2.079$
D) $\ln 8 \approx 0.079$
E) $\ln 8 \approx 4.079$

Question 78

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\ln \sqrt { x - 8 } = 7$

A) $e ^ { 14 } + 8 \approx 1,202,611.284$
B) $e ^ { 14 } + 8 \approx 1,202,614.284$
C) $e ^ { 14 } + 8 \approx 1,202,612.284$
D) $e ^ { 14 } + 8 \approx 1,202,610.284$
E) $e ^ { 14 } + 8 \approx 1,202,613.284$

Question 79

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $9 + 2 \ln x = 4$

A) $e ^ { - 5 / 2 } \approx 1.082$
B) $e ^ { - 5 / 2 } \approx - 0.918$
C) $e ^ { - 5 / 2 } \approx - 1.918$
D) $e ^ { - 5 / 2 } \approx 0.082$
E) $e ^ { - 5 / 2 } \approx 2.082$

Question 80

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $\ln x - 5 = 0$

A) $e ^ { 5 } \approx 151.413$
B) $e ^ { 5 } \approx 146.413$
C) $e ^ { 5 } \approx 148.413$
D) $e ^ { 5 } \approx 149.413$
E) $e ^ { 5 } \approx 150.413$