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Sonja and Chris both accept new jobs on March 1, 2001. Sonja starts at $47,000

Question : Sonja and Chris both accept new jobs on March 1, 2001. Sonja starts at $47,000 : 2151546

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Write the expression using base e rather than base 10.

1) 10x + 7

A) 10ex + 7

B) e(ln10)(x + 7)

C) e10(x + 7)

D) (x + 7)e10

2) 10x^6

A) e10x^6

B) 10ex^6

C) e(ln10)x^6

D) x6e10

Approximate the expression in the form ax without using e. Round to the nearest thousandth when necessary.

3) e7x

A) 1.946x

B) 198.251x

C) 1096.633x

D) 19.028x

4) e-7x

A) -1.946x

B) 0.388x

C) -19.028x

D) 0.001x

Find the domain of the function.

5) f(x) =log(x - 2)

A) x > 1

B) x > 0

C) x > 2

D) x > -2

6) f(x) = ln(10 - x)

A) x > -10

B) x > 10

C) x < -10

D) x < 10

7) f(x) =log9(25 - x2)

A) -5 < x < 5

B) -5 ≤ x ≤ 5

C) -25 < x < 25

D) x < -5 and x > 5

8) f(x) = ln(4x - x2)

A) 0 < x < 4

B) x ≤ 4

C) -4 ≤ x < 0

D) -4 < x < 4

Solve the problem.

9) Sonja and Chris both accept new jobs on March 1, 2001. Sonja starts at $47,000 with a raise each March 1 of 3%. Chris starts at $28,000 with a raise on March 1 of each year of 8%. In what year will Chris' salary exceed Sonja's?

A) 2011

B) 2013

C) 2012

D) 2010

10) A college student invests $7000 in an account paying 7% per year compounded annually. In how many years will the amount at least double? Round to the nearest tenth when necessary.

A) 13.5 yr

B) 18.5 yr

C) 10.2 yr

D) 16.2 yr

11) How long will it take for prices in the economy to double at a 5% annual inflation rate? Round to the nearest hundredth when necessary.

A) 11.9 yr

B) 23.45 yr

C) 22.52 yr

D) 14.21 yr

12) Assume the cost of a car is $19,000. With continuous compounding in effect, find the number of years it would take to double the cost of the car at an annual inflation rate of 6%. Round to the nearest hundredth.

A) 164.20 yr

B) 175.76 yr

C) 11.55 yr

D) 1.64 yr

13) Suppose the consumption of electricity grows at 3% per year, compounded continuously. Find the number of years before the use of electricity has tripled. Round to the nearest hundredth.

A) 3.66 yr

B) 36.62 yr

C) 100.00 yr

D) 0.37 yr

14) The purchasing power of a dollar is decreasing at the rate of 5% annually, compounded continuously. How long will it take for the purchasing power of $1.00 to be worth $0.64? Round to the nearest hundredth.

A) 12.80 yr

B) 8.93 yr

C) 0.89 yr

D) 0.09 yr

15) At what interest rate must $5900 be compounded annually to equal $9152.84 after 9 years? Round to the nearest percent.

A) 5%

B) 7%

C) 4%

D) 6%

16) Kimberly invested $5000 in her savings account for 7 years. When she withdrew it, she had $7145.18. Interest was compounded continuously. What was the interest rate on the account? Round to the nearest tenth of a percent when necessary.

A) 5.2%

B) 5.1%

C) 5.25%

D) 5%

17) The magnitude of an earthquake, measured on the Richter scale, is given by R(I) =log(I/I0), where I is the amplitude registered on a seismograph located 100 km from the epicenter of the earthquake, and I0 is the amplitude of a certain small size earthquake. Find the Richter scale rating of an earthquake with an amplitude of 19,953I0.

A) 4.3

B) 3.3

C) 9.9

D) 0.43

18) The magnitude of an earthquake, measured on the Richter scale, is given by R(I) =log(I/I0), where I is the amplitude registered on a seismograph located 100 km from the epicenter of the earthquake, and I0 is the amplitude of a certain small size earthquake. An earthquake measured 7.9 on the Richter scale. Express this reading in terms of I0.

A) 63,095,734I0

B) 2695I0

C) 79,432,823I0

D) 7,943,282I0

19) The magnitude of an earthquake, measured on the Richter scale, is given by R(I) =log(I/I0), where I is the amplitude registered on a seismograph located 100 km from the epicenter of the earthquake, and I0 is the amplitude of a certain small size earthquake. Find the Richter scale rating of an earthquake with an amplitude of 108.1I0.

A) 8.1

B) 18.7

C) 18.1

D) 1.9

20) A certain noise has intensity 9.56 × 108I0. What is the decibel rating of this sound? Use the formula D = 10logI0, where I0 is a faint threshold sound, and I is the intensity of the sound.”

A) 80 decibels

B) 207 decibels

C) 9 decibels

D) 90 decibels

21) The pH of a solution is defined as pH = -log[H+], where [H+] is the concentration of hydrogen ions in the solution. The pH of pure water is 7, while the pH of stomach acid is about 1. How much greater is the concentration of hydrogen ions in stomach acid than in pure water?

A) 6 times greater

B) 1,000,000 times greater

C) 100,000 times greater

D) 100 times greater

22) An RC circuit is a simple electronic circuit consisting of a resistor, a capacitor, and a battery. The current i in the circuit at some time t after the battery is connected is i = (V/R)e-t/(RC), where V is the battery's voltage, R is the resistance, and C is the capacitance. Solve this equation for C.

A) C = (-R/tln((iR/V)))

B) C = (t/Rln((V/iR)))

C) C = (Ve-t/R2C)

D) C = (V/R)e-t/(iR)

23) One hundred rats are being trained to run through a maze and are rewarded when they run through it correctly. Once a rat successfully runs the maze, it continues to run the maze correctly in all subsequent trials. The number of rats that run the maze incorrectly after t attempts is given approximately by N(t) = 100e-.14t. Find the number of trials required such that only 45% of the rats are running the maze incorrectly. Round to the nearest trial.

A) 23 trials

B) 27 trials

C) 6 trials

D) 5 trials

24) The population growth of an animal species is described by F(t) = 900 + 70log3(2t + 1) where t is measured in months. Find the population of this species in an area 13 month(s) after the species is introduced.

A) 1110

B) 565

C) 2790

D) 1415

25) Coyotes are one of the few species of North American animals with an expanding range. The future population of coyotes in a region of Mississippi can be modeled by the equation P = 41 + 16ln(13t + 1), where t is time in years. Use the equation to determine when the population will reach 160. (Round to the nearest tenth of a year.)

A) 130.7 yr

B) 130.9 yr

C) 2,106,476.6 yr

D) 130.6 yr

Solution
5 (1 Ratings )

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