Deck 10: The Nature of Growth

Question 1

Find a simplified value for x by inspection. Do not use a calculator. ​ ​

A) 243
B) 81
C) 7
D) 4
E) 5

Answer 1

5

Question 2

The radioactive substance neptunium -139 decays to 72.85% of its original amount after 28 hours. How long (to the nearest hour) would it take for 37% of the original neptunium to be present?
​
__________ hours

Answer 2

88

Question 3

Nashville had a population of 458,699 in 1980 and 494,850 in 1990. Predict the population in Nashville in 1994. ​

A) 509,592
B) 510,404
C) 510,096
D) 510,903
E) 501,414

Answer 3

510,096

Question 4

A rock concert was measured to be watta/cm². Find the number of decibels for the power of the sound and round it to the nearest decibel. ​

A) 100 dB
B) 107 dB
C) 109 dB
D) 121 dB
E) 104 dB

Question 5

Nashville had a population of 545,524 in 2000 and 559,918 in 2002. Predict the population in Nashville in 2006.
​
Please round your answer to the nearest whole.

Question 6

A satellite has an initial radioisotope power supply of 65 watts (W). The power output in watts is given by ​ ​
Where t is the time in days. Solve for t to find the time when the power supply is 26 W.
​

A) 243 days
B) 250 days
C) 99 days
D) 229 days
E) 222 days

Question 7

A bacteria culture had a population of 10 million at 10:00
A.M., and by 2:00 P.M. had grown to 16 million. Predict the population at 6:00 P.M. that same day.
​
Please round your answer to the nearest tenth of a million.
​
__________ million

Question 8

Tests of an artifact discovered at the Debert site in Nova Scotia show that 31% of the original is still present. What is the probable age of the artifact?
​
(Use )
​
Please round your answer to the nearest whole.
​
__________ years old

Question 9

A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of . Find this earthquake's magnitude.
​
Please round your answer to the nearest tenth.

Question 10

The radioactive substance neptunium-139 decays to 73.64% of its original amount after 24 hours. How long (to the nearest hour) would it take for 39% of the original neptunium to be present? ​

A) 83 hr
B) 77 hr
C) 39 hr
D) 74 hr
E) 68 hr

Question 11

The atmospheric pressure P in pounds per square inch (psi) is given by the formula below, where a is the altitude above sea level (in miles). If a city has an atmospheric pressure of 13.16 psi, what is its altitude?
​ ​
Please round your answer to the nearest foot.
​
__________ ft

Question 12

Compare the amount of earth movement (energy released) by earthquakes of magnitudes 4 and 8.
​
Please round your answer to the nearest whole.
​
One earthquake releases __________ times more energy than the other one.

Question 13

The atmospheric pressure P in pounds per square inch (psi) is given by ​ ​
Where a is the altitude above sea level (in miles). If a city has an atmospheric pressure of 13.27 psi, what is its altitude?
​

A) 2,565 ft
B) 3,038 ft
C) 2,549 ft
D) 2,573 ft
E) 2,557 ft

Question 14

A rock concert was measured to be watts/cm². Find the number of decibels for the power of the sound and round it to the nearest decibel.
​
__________ dB

Question 15

Compare the strengths of earthquakes with magnitudes 2 and 3.
​
One earthquake is __________ times stronger than the other.

Question 16

A satellite has an initial radioisotope power supply of 80 watts (W). The power output in watts is given by the formula below, where t is the time in days. Solve for t to find the time when the power supply is 25W.
​ ​
Please round your answer to the nearest whole.
​
t = __________ days

Question 17

Compare the amount of earth movement (energy released) by earthquakes of magnitudes 3 and 6. ​

A) 1,000 times more energy
B) 10 times more energy
C) 5,623 times more energy
D) 31,623 times more energy
E) 1,000,000 times more energy

Question 18

A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of . Find this earthquake's magnitude. ​

A) M = 3.8
B) M = 7.8
C) M = 6.5
D) M = 7.1
E) M = 8.7

Question 19

Tests of an artifact discovered at the Debert site in Nova Scotia show that 25% of the original ¹⁴ C is still present. What is the probable age of the artifact? (Use r = -1.20968 ´ 10^-4 ) ​

A) 4,977 yr old
B) 11,460 yr old
C) 10,487 yr old
D) 11,082 yr old
E) 10,931 yr old

Question 20

Compare the strengths of earthquakes with magnitudes 5 and 8. ​

A) The one with a magnitude 8 is 160 times stronger than the one with magnitude 5.
B) The one with a magnitude 8 is 1,000 times stronger than the one with magnitude 5.
C) The one with a magnitude 8 is 100 times stronger than the one with magnitude 5.
D) The one with a magnitude 8 is 1.6 times stronger than the one with magnitude 5.
E) The one with a magnitude 8 is 10 times stronger than the one with magnitude 5.

Question 21

Find a simplified value for x by inspection. Do not use a calculator.
​ __________

Question 22

An advertising agency conducted a survey and found that the number of units sold, N, is related to the amount a spent on advertising (in dollars) by the following formula: ​ ​
How many units are sold after spending $8,000?
​

A)
B)
C)
D)
E)

Question 23

Use the properties of logarithms to write each expression as a single logarithm with a coefficient of 1.
​

Question 24

Solve the equations by finding the exact solution.
​

Question 25

The "forgetting curve" for memorizing nonsense syllables is given by ​ , ,
​
Where R is the percentage who remember the syllables after t seconds.
​
In how many seconds to the nearest second would only 15 % of the students remember?
​

A)
B)
C)
D)
E)

Question 26

The "forgetting curve" for memorizing nonsense syllables is given by equation below, where R is the percentage who remember the syllables after t seconds.
​ , ​
In how many seconds would only 10% of the students remember? Round your answer to the nearest second.
​
Solve for the exact value of t in terms of R.

Question 27

Use the definition of logarithm to simplify the expression. ​ ​

A) 0
B) ​
C)
D)
E) 7

Question 28

Write the equation in logarithmic form. ​ ​

A)
B)
C)
D)
E)

Question 29

Solve the following equation by finding the exact solution. ​ ​

A)
B)
C)
D)
E)

Question 30

Find a simplified value for x by inspection. Do not use a calculator. ​ ​

A)
B) 132
C) 120
D) 139
E)

Question 31

Use the properties of logarithms to write the following expression as a single logarithm with a coefficient of 1. ​ ​

A)
B)
C)
D)
E)

Question 32

Solve the equations by finding the exact solution. ​ ​

A)
B)
C)
D)
E)

Question 33

Use the properties of logarithms to write the following expression as a single logarithm with a coefficient of 1.
​

Question 34

Solve the following equation by finding the exact solution.
​

Question 35

Solve the following equation by finding the exact solution.
​

Question 36

Solve the following equation by finding the exact solution. ​ ​

A)
B)
C)
D)
E)

Question 37

An advertising agency conducted a survey and found that the number of units sold, N, is related to the amount a spent on advertising (in dollars) by the following formula:
​ ​
How many units are sold after spending $3,000? $__________ (Round your answer to the nearest unit)
​
How many units are sold after spending $38,000? $__________ (Round your answer to the nearest unit)
​
How much needs to be spent (to the nearest hundred dollars) to sell 4,000 units? $__________

Question 38

Find a simplified value for x by inspection. Do not use a calculator.
​ ​
x = __________

Question 39

Use the properties of logarithms to write the expression as a single logarithm with a coefficient of 1. ​ ​

A)
B)
C)
D)
E)

Question 40

Solve the exponential equation below, and give the exact value for x. ​ ​

A)
B)
C)
D)
E)

Question 41

Solve the exponential equation.
​ ​
x = __________

Question 42

Write the expression below in terms of natural logarithms, and then give a calculator approximation (correct to four decimal places). ​ ​

A)
B)
C)
D)
E)

Question 43

Write the expression below in terms of natural logarithms.
​ ​
Give a calculator approximation (correct to four decimal places).

Question 44

Write the expression below in terms of common logarithms.
​ ​
Give a calculator approximation (correct to four decimal places).

Question 45

Solve the exponential equation. ​ ​

A)
B)
C)
D)
E)

Question 46

Solve the exponential equation below, and give the exact value for .
​

Question 47

Solve the exponential equation.
​ ​
Round your answer to four decimal places, if required.
​
x = __________

Question 48

Use the definition of logarithm to simplify the expression.
​

Question 49

Write the equation in logarithmic form.
​

Question 50

If the earth's radius is approximately 3,963 miles, and if a hypothetical perpetual water-making machine pours out 32 gallons in the first minute and then doubles its capacity each minute, how long would it take for this hypothetical machine to fill up the earth with water? ​

A) 1 hr 15 min
B) 1 hr 12 min
C) 1 hr 17 min
D) 1 hr 13 min
E) 1 hr 10 min

Question 51

Write the expression below in terms of common logarithms, and then give a calculator approximation (correct to four decimal places). ​ ​

A)
B)
C)
D)
E)

Question 52

Evaluate the expression below to two decimal places. ​ ​

A) 0.65
B) 0.52
C) 0.56
D) 0.82
E) 1.50

Question 53

Evaluate the expression below to two decimal places.
​

Question 54

Solve the exponential equation. ​ ​

A)
B)
C)
D)
E)

Question 55

Solve the exponential equation below.
​ ​
Round your answer to four decimal places.

Question 56

If the earth's radius is approximately 3,963 miles, and if a hypothetical perpetual water-making machine pours out 32 gallons in the first minute and then doubles its capacity each minute, how long would it take for this hypothetical machine to fill up the earth with water?
​
__________ hr. __________ min.

Question 57

Solve the exponential equation below. ​ ​

A)
B)
C)
D)
E)