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# Intro to Exponential Functions - PowerPoint PPT Presentation

Intro to Exponential Functions. Lesson 3.1. Contrast. View differences using spreadsheet. Contrast. Suppose you have a choice of two different jobs at graduation Start at \$30,000 with a 6% per year increase Start at \$40,000 with \$1200 per year raise Which should you choose?

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## PowerPoint Slideshow about ' Intro to Exponential Functions' - hyacinth-hoffman

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### Intro to Exponential Functions

Lesson 3.1

• Suppose you have a choice of two different jobs at graduation

• Start at \$30,000 with a 6% per year increase

• Start at \$40,000 with \$1200 per year raise

• Which should you choose?

• One is linear growth

• One is exponential growth

• How do we get each nextvalue for Option A?

• When is Option A better?

• When is Option B better?

• Rate of increase a constant \$1200

• Rate of increase changing

• Percent of increase is a constant

• Ratio of successive years is 1.06

• Consider a savings account with compounded yearly income

• You have \$100 in the account

• You receive 5% annual interest

View completed table

• Completed table

• Table of results from calculator

• Set y= screen y1(x)=100*1.05^x

• Choose Table (Diamond Y)

• Graph of results

• Population growth often modeled by exponential function

• Half life of radioactive materials modeled by exponential function

• Recall formulanew balance = old balance + 0.05 * old balance

• Another way of writing the formulanew balance = 1.05 * old balance

• Why equivalent?

• Growth factor: 1 + interest rate as a fraction

• Consider a medication

• Patient takes 100 mg

• Once it is taken, body filters medication out over period of time

• Suppose it removes 15% of what is present in the blood stream every hour

Fill in the rest of the table

What is the growth factor?

• Completed chart

• Graph

Growth Factor = 0.85

Note: when growth factor < 1, exponential is a decreasing function

• For our medication example when does the amount of medication amount to less than 5 mg

• Graph the functionfor 0 < t < 25

• Use the graph todetermine when

• All exponential functions have the general format:

• Where

• A = initial value

• B = growth factor

• t = number of time periods

• When B > 1

• When B < 1

View results of B>1, B<1 with spreadsheet

• Lesson 3.1A

• Page 112

• Exercises1 – 23 odd

• Lesson 3.1B

• Pg 113

• Exercises25 – 37 odd