Section 5.5

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Section 5.5 Exponential and Logarithmic Models
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• A savings account is opened with 20,000 earning
  10.5
• compounded continuously.
• a. How many years does it take for the money to
  double?
• b. How much is in the account after ten years?

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• A savings account is opened with 600. At the
  end of ten
• years, the account will have 19205. If the
  account earns
• interest compounded continuously
• a. What is the annual percentage rate of
  interest?
• b. How many years did it take for the account
  to double in value?

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• Given determine the
  principal P that must be
• invested that must be invested at 12 so
  that 500,000 will be available in 40 years.
•  

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• The population P of a city is
  where t 0
• represents the year 2000. According to
  this model, when
• will the population reach 275000?

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• The number of bacteria N in a culture is modeled
  by
• , where t is the time in
  hours. If N 300 when t 5,
• estimate the time required for the population
  to double in size.

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7. A car that cost 22,000 new has a book value
of 13,000 after 2 years. a. Find the
straight-line model V mt b b. Find the
exponential model
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7. A car that cost 22,000 new has a book value
of 13,000 after 2 years. c. Use a graphing
utility to graph the two models in the same
viewing window. Which model depreciates faster
in the first two years? d. Find the book values
of the car after 1 year and after 3 years using
each model.
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8. The sales S (in thousands of units) of a new
product after it has been on the market t years
are modeled by .
15000 units of the new product were sold the
first year. a. Complete the model by solving
for k. b. Use the model to estimate the number
of units sold after five years.  
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9. The sales S (in thousands of units) of a
product after x hundred dollars is spend on
advertising are modeled by
. When 500 is spend on advertising, 2500 units
are sold. a. Complete the model by solving for
k. b. Estimate the number of units that will be
sold if advertising expenditures are raised to
700.
3315
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10. The management at a factory has found that
the maximum number of units a worker can produce
in a day is 30. The learning curve for the
number of units N produced per day after a new
employee has worked t days is
. After 20 days on the job, a new employee
produces 19 units. a. Find the learning curve
for this employee (first, find the value
of k). b. How many days should pass before this
employee is producing 25 units per
day? c. Is the employees production increasing
at a linear rate? Explain your reasoning.
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10. The management at a factory has found that
the maximum number of units a worker can produce
in a day is 30. The learning curve for the
number of units N produced per day after a new
employee has worked t days is
. After 20 days on the job, a new employee
produces 19 units. a. Find the learning curve
for this employee (first, find the value
of k). b. How many days should pass before this
employee is producing 25 units per
day? c. Is the employees production increasing
at a linear rate? Explain your reasoning.
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• On the Richter scale, the magnitude R of an
  earthquake of
• intensity I is where
  is the minimum
• intensity used for comparison. Find the
  magnitude R of an earthquake of intensity I if
• a. I 80500000
• b. I 48275000
• c. 251,200
•