# 2.1: Modeling Data

**At Grade**Created by: CK-12

*This activity is intended to supplement Calculus, Chapter 1, Lesson 3.*

## Problem 1 – Exponential Growth

When Connor was born, his parents put \begin{align*}\$1,000\end{align*}

Enter the data to the right in \begin{align*}L1\end{align*}**STAT ENTER.**

Create a scatter plot of the data by pressing \begin{align*}2^{nd} \ [Y=]\end{align*}**ENTER** and matching the screen to the right.

To view the scatter plot, press **ZOOM** and select **9:ZoomStat**.

Using your knowledge of compound interest, study the data and the graph to determine a function for the growth of Connor’s money.

Enter your equation in \begin{align*}Y1\end{align*}**GRAPH** to check your result.

Note: the regressions can be found by pressing **STAT** and scrolling over to the **CALC** menu. Select ExpReg, **ENTER** \begin{align*}2^{nd}\end{align*}**ENTER**.

The equation for the data is: ______________

## Problem 2 – Logarithmic Growth

Scientists are testing the amount of greenhouse gases present at a research site near the north pole to determine the effect on polar ice melting. Enter in the results in \begin{align*}L3\end{align*}

Create a scatter plot of the data by pressing \begin{align*}2^{nd} \ [Y=]\end{align*}**1:Plot1**, and matching the screen to the right.

To view the scatter plot, press **ZOOM** and select **9:ZoomStat**.

Note: \begin{align*}L3\end{align*}

Determine a natural log equation to model the data by pressing **STAT**, scrolling over to **CALC** and selecting **9:LnReg**.

To finish the regression, enter, \begin{align*}L3, L4, Y1\end{align*}**LnReg** \begin{align*}L3, L4, Y1\end{align*}

Press **GRAPH** to view the scatter plot and regression equation both plotted.

The equation for the data is: ______________

## Extension – Exponential Decay

*You will need to download L5.8xl and L6.8xl from your teacher for this extension*.

Due to an environmental spill, a farmer is losing the amount of land on which he can plant crops. The data in \begin{align*}L5\end{align*}

After creating a scatter plot of the data, use your graphing calculator to perform an exponential regression that models the data and plot the function by pressing **GRAPH.**

The equation for the data is: ______________

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