Applications of Exponential and Logarithmic functions

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Applications of Exponential and Logarithmic
functions
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Solving a word problem using an exponential
equation Problem type 2 A principal of
             is invested at            
interest, compounded annually. How many years
will it take to accumulate              or more
in the account? (Use the calculator provided if
necessary.) Write the answer as a whole number.
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Exponential Growth/Decay Model
Initial Amount A amount after time t r
growth/decay rate Growth r positive Decay
r negative
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Solving a word problem using an exponential
equation Problem type 3 The number of bacteria
in a certain population increases according to an
exponential growth model, with a growth rate of
         per hour. An initial sample is obtained
from this population, and after five hours, the
sample has grown to                 bacteria.
Find the number of bacteria in the initial
sample. Round your answer to the nearest integer.

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• The population of a colony of mosquitoes follows
  the exponential growth model. If there are 1000
  mosquitoes present initially and there are 1800
  after 2 days,
• What is the growth rate?
• What will be the size of the colony after 5 days?
• How long will it take for the size to reach
  10,000?

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Half-life of a radioactive substance is the time
required for half of the radioactive substance to
decay.
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• The half-life of radium is 1690 years. If 10
  grams is present now, how much will be present in
  50 years?

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• A piece of charcoal is found to contain 30 of
  the carbon 14 that it originally had. When did
  the tree from which the charcoal came die? Use
  5600 years as the half-life of carbon 14.