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A wooden artifact from an archeological dig contains 60 percent of the carbon-14 that is present in living trees. To the nearest year, about how many years old is the artifact? (The half-life of carbon-14 is 573 0 years.)

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A research student is working with a culture of bacteria that doubles in size every twenty minutes. The initial population count was 1350 bacteria. Rounding to five significant digits, write an exponential equation representing this situation. To the nearest whole number, what is the population size after  3  hours?

f ( t ) = 1350 e ( 0.03466 t ) ; after 3 hours: P ( 180 ) 691 , 200

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For the following exercises, use this scenario: A biologist recorded a count of 360 bacteria present in a culture after 5 minutes and 1000 bacteria present after 20 minutes.

To the nearest whole number, what was the initial population in the culture?

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Rounding to six significant digits, write an exponential equation representing this situation. To the nearest minute, how long did it take the population to double?

f ( t ) = 256 e ( 0.068110 t ) ; doubling time: about 10 minutes

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For the following exercises, use this scenario: A pot of boiling soup with an internal temperature of 100° Fahrenheit was taken off the stove to cool in a 69° F room. After fifteen minutes, the internal temperature of the soup was 95° F .

Use Newton’s Law of Cooling to write a formula that models this situation.

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To the nearest minute, how long will it take the soup to cool to 80° F?

about 88 minutes

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To the nearest degree, what will the temperature be after 2 and a half hours?

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For the following exercises, use this scenario: A turkey is taken out of the oven with an internal temperature of 165°F and is allowed to cool in a 75°F room. After half an hour, the internal temperature of the turkey is 145°F .

Write a formula that models this situation.

T ( t ) = 90 e ( 0.008377 t ) + 75 , where t is in minutes.

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To the nearest degree, what will the temperature be after 50 minutes?

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To the nearest minute, how long will it take the turkey to cool to 110° F?

about 113 minutes

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For the following exercises, find the value of the number shown on each logarithmic scale. Round all answers to the nearest thousandth.

Number line to show log(x) is between 1 and 2.

log ( x ) = 1.5 ; x 31.623

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Plot each set of approximate values of intensity of sounds on a logarithmic scale: Whisper: 10 10   W m 2 , Vacuum: 10 4 W m 2 , Jet: 10 2   W m 2

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Recall the formula for calculating the magnitude of an earthquake, M = 2 3 log ( S S 0 ) . One earthquake has magnitude 3 . 9 on the MMS scale. If a second earthquake has 75 0 times as much energy as the first, find the magnitude of the second quake. Round to the nearest hundredth.

MMS magnitude: 5.82

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For the following exercises, use this scenario: The equation N ( t ) = 500 1 + 49 e 0.7 t models the number of people in a town who have heard a rumor after t days.

How many people started the rumor?

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To the nearest whole number, how many people will have heard the rumor after 3 days?

N ( 3 ) 71

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As t increases without bound, what value does N ( t ) approach? Interpret your answer.

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For the following exercise, choose the correct answer choice.

A doctor and injects a patient with 13 milligrams of radioactive dye that decays exponentially. After 12 minutes, there are 4.75 milligrams of dye remaining in the patient’s system. Which is an appropriate model for this situation?

  1. f ( t ) = 13 ( 0.0805 ) t
  2. f ( t ) = 13 e 0.9195 t
  3. f ( t ) = 13 e ( 0.0839 t )
  4. f ( t ) = 4.75 1 + 13 e 0.83925 t

C

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Practice Key Terms 6

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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