# HOW THE CONCEPT OF EXPONENTIAL FUNCTIONS THAT CAN BE USED TO MODEL GROWTH AND DECAY.

HOW THE CONCEPT OF EXPONENTIAL FUNCTIONS THAT CAN BE USED TO MODEL GROWTH AND DECAY.

Assignment 1: LASA 2: Exponential Growth

In Module 4, you were introduced to the concept of exponential functions that can be used to model growth and decay. Recall what you learned in The Number e lecture. In this exercise, you will use a Microsoft Excel spreadsheet to calculate the exponential growth of a population of your choosing. (If you use the linked spreadsheet below, it is recommended that you consider relatively small populations and not those of entire nations.)

Click here to open the Microsoft Excel spreadsheet that you will use to perform the calculations for this assignment.

In the spreadsheet, perform the following operations: 1.Input a population value into the box next to Initial Population on the spreadsheet. This population should be anything such as the people, animals, microorganisms, or plants. 2.Input a rate of growth for your population into the box next to Rate 1. Since we are interested in a positive annual percent growth rate per year, this number should be greater than zero percent. Be sure to input this number in the form of a decimal. 3.Repeat the above procedure for Rate 2 and Rate 3. Make sure that the values you select differ by two percent. For example, the values 0.01, 0.03, and 0.05 would be good choices. 4.Under the Time (years) column, input three different year values. Make sure that your values increase by a minimum of ten years. For example, 10, 20, 30 years would be good choices. If you want to see a more dramatic change, select a longer time frame such as 10, 50, and 100 years. 5.When you input all of your data, you’ll see that the spreadsheet has performed the calculations for the future size of each population, rate of growth, and time interval. Additionally, this information will be presented graphically in the chart. To draw an exponential curve for each series, do the following: a.Right click on the middle point for one of the series. b.Click on add trendline. c.Under Trendline Options, select Exponential. d.Click Close e.Repeat these steps for the other series.

Now that you’ve completed your analysis, it is now time to report the results and examine your findings.

In a Microsoft Word document, respond to the following: 1.Calculate what the future size of the population will be, given a specific initial population, rate of growth, and time interval.

Use the exponential equation: Future value = Present value * exp(rt) ◦exp is the base “e” ◦r = annual rate of growth expressed as a percent ◦t = years 