A more realistic scenario

At some point, you’re going to invest money in a bank, and will set up a savings account that accrues interest.

Write equations for the following scenarios:

Initial investment of $15,000 earning 4% interest compounded annually

Initial investment of $5,000 earning 12% interest compounded annually

Initial investment of $10,000 earning 8% interest compounded annually

Which of the scenarios nets more money after 5 years? 12 years? 20 years?

Recall from the linear unit that we could find a line of best fit, or a regression line, using a calculator and the following steps:

Step 1: STAT and EDIT to plug our values in

Step 2: STAT →CALC Step 3: Press 4: LinReg(ax+b) Step 4: Calculate We can perform a similar process to find

the exponential regression model. To find the answer, we can go to 0: ExpReg

This allows the calculator to do the legwork in helping us to find out what the equation is.

Real Life Scenario Growth in animal populations can be

predicted by exponential equations. However, we may not be able to observe percent growth rates, which may not be constant from year to year.

One way to circumvent this is to use an exponential regression line.

An important point concerning exponential regression lines is that you must be able to recognize when an exponential regression model is necessary instead of a linear regression model

Suppose that census counts of coyotes in western NC began in 2000 and produced these estimates for several different years.

Plot the wolf population data and decide whether a linear or exponential function seems likely to match the pattern of growth well. (You may plot this in your calculator.)

Use your calculator to find both a linear regression model and an exponential regression model for the data pattern.

Which of your regression models appears to best fit the data?

Use what you think is the better model to calculate population estimates for the missing years 2004 and 2011, and then for the years 2025 and 2030.

Time Since 1990 (in years)

0 2 5 7 10 13

Estimated Coyote Population

100 300 500 900 1,500

3,100

Consider the following data from the International Shark Attack File from the University of Florida dealing with documented worldwide shark attacks. Site can be accessed here

Plot the given shark attack data in your graphing calculator. Decide what type of function seems likely to match the data well.

Use your calculator to find both linear and exponential regression models for the data pattern.

Which of your models seems to best fit the data pattern? Use the data model you think best fits the data to calculate

documented shark attack estimates for the 1960s, 2010s, and 2040s.

Decades since 1900

0 2 4 6 9 10Number of Attacks

30 80 100 220 500 650