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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 13, 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*}
4log(x5)+log(6254)=2logx 
\begin{align*}log_5 z + \frac{log_5 125}{log_5 x} = \frac{7}{2}\end{align*}
log5z+log5125log5x=72 
\begin{align*}log p = \frac{2  log p}{log p}\end{align*}
logp=2−logplogp 
\begin{align*}2 log x  2 log (x+1) = 0\end{align*}
2logx−2log(x+1)=0 
\begin{align*}log (25  z^3)  3log (4  z) = 0\end{align*}
log(25−z3)−3log(4−z)=0 
\begin{align*}\frac{log (35  y^3)}{log (5  y)} = 3\end{align*}
log(35−y3)log(5−y)=3
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