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Exponential Models

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Exponential and Logarithmic Models
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Vocabulary

Complete the table.
Word Definition
______________ to create new data points, or to predict, outside of the domain of the data set
Interpolate ______________________________________________________________________
______________ a solution to a function that is not useful in the given context
Exponential Model ______________________________________________________________________

Models

A population which increases continuously at a constant rate may be modeled with an exponential function.

A population which increases rapidly and then levels off may be modeled with a logarithmic function.

Exponential

The equation for population growth is: P(f) = P_i \cdot r^{x} 

What does each letter in the equation mean? ______________  ______________  ______________  ______________

This equation is used in countless situations besides population growth. What are some situations in which you would use that equation? ________________________________________________________

.

For problems 1-3, calculate:

a) The growth factor

b) The final population

  1. If a population starts at 5,000 people in 1990, and increases at a rate of 9% per year, what is the population in 2037?
  2. If a population starts at 15,000 people in 2000, and increases at a rate of 6% per year, what is the population in 2019?
  3. If a population starts at 25,500 people in 1900, and increases at a rate of 4% per year, what is the population in 2004?
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Logarithmic

To solve complex logarithmic equations, you must use your knowledge from algebra as well as the logarithmic properties

What are three logarithmic properties?

1) ____________________________________

2) ____________________________________

3) ____________________________________

.

Solve for x

  1. 4 log (\frac{x}{5}) + log (\frac{625}{4}) = 2 log x
  2. log_5 z + \frac{log_5 125}{log_5 x} = \frac{7}{2}
  3. log p = \frac{2 - log p}{log p}
  4. 2 log x - 2 log (x+1) = 0
  5. log (25 - z^3) - 3log (4 - z) = 0
  6. \frac{log (35 - y^3)}{log (5 - y)} = 3


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