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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: \begin{align*}P(f) = P_i \cdot r^{x}\end{align*}

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

- 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?
- 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?
- 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?

#### 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 \begin{align*}x\end{align*}**

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

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