<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />

Exponential Models

Population and investing using exponential functions.

Estimated8 minsto complete
%
Progress
Practice Exponential Models
Progress
Estimated8 minsto complete
%
Exponential and Logarithmic Models

Feel free to modify and personalize this study guide by clicking “Customize.”

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)=Pirx\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

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?

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

1. 4log(x5)+log(6254)=2logx\begin{align*}4 log (\frac{x}{5}) + log (\frac{625}{4}) = 2 log x\end{align*}
2. log5z+log5125log5x=72\begin{align*}log_5 z + \frac{log_5 125}{log_5 x} = \frac{7}{2}\end{align*}
3. logp=2logplogp\begin{align*}log p = \frac{2 - log p}{log p}\end{align*}
4. 2logx2log(x+1)=0\begin{align*}2 log x - 2 log (x+1) = 0\end{align*}
5. log(25z3)3log(4z)=0\begin{align*}log (25 - z^3) - 3log (4 - z) = 0\end{align*}
6. log(35y3)log(5y)=3\begin{align*}\frac{log (35 - y^3)}{log (5 - y)} = 3\end{align*}

My Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes