Exponential Growth & Decay Applications that Apply to Me!

Exponential Function What do we know about exponents? What do we know about functions?

Exponential Functions Always involves the equation: bx Example: 23 = 2 · 2 · 2 = 8

Group investigation: Y = 2x Create an x,y table. Use x values of -1, 0, 1, 2, 3, Graph the table What do you observe.

The Table: Results X F(x) = 2x -1 2-1 = ½ 20 = 1 1 21 = 2 2 22 = 4 3 20 = 1 1 21 = 2 2 22 = 4 3 23 = 8

The Graph of y = 2x

Observations What did you notice? What is the pattern? What would happen if x= -2 What would happen if x = 5 What real-life applications are there?

Group: Money Doubling? You have a $100.00 Your money doubles each year. How much do you have in 5 years? Show work.

Money Doubling Year 1: $100 · 2 = $200 Year 2: $200 · 2 = $400 Year 3: $400 · 2 = $800 Year 4: $800 · 2 = $1600 Year 5: $1600 · 2 = $3200

Earning Interest on You have $100.00. Each year you earn 10% interest. How much $ do you have in 5 years? Show Work.

Earning 10% results Year 1: $100 + 100·(.10) = $110

Growth Models: Investing The Equation is: A = P (1+ r)t P = Principal r = Annual Rate t = Number of years

Using the Equation $100.00 10% interest 5 years 100(1+.10)5 = $161.05 What could we figure out now?

Comparing Investments Choice 1 $10,000 5.5% interest 9 years Choice 2 $8,000 6.5% interest 10 years

Choice 1 $10,000, 5.5% interest for 9 years. Equation: $10,000 (1 + .055)9   Balance after 9 years: $16,190.94

Choice 2 $8,000 in an account that pays 6.5% interest for 10 years.   Equation: $8,000 (1 + .065)10 Balance after 10 years: $15,071.10

The first one yields more money. Which Investment? The first one yields more money. Choice 1: $16,190.94 Choice 2: $15,071.10

Instead of increasing, it is decreasing. Exponential Decay Instead of increasing, it is decreasing. Formula: y = a (1 – r)t a = initial amount r = percent decrease t = Number of years

Real-life Examples What is car depreciation? Car Value = $20,000 Depreciates 10% a year Figure out the following values: After 2 years After 5 years After 8 years After 10 years

Exponential Decay: Car Depreciation Assume the car was purchased for $20,000 Depreciation Rate Value after 2 years Value after 5 years Value after 8 years Value after 10 years 10% $16,200 $11,809.80 $8609.34 $6973.57 Formula: y = a (1 – r)t a = initial amount r = percent decrease t = Number of years

What Else? What happens when the depreciation rate changes. What happens to the values after 20 or 30 years out – does it make sense? What are the pros and cons of buying new or used cars.

Assignment 2 Worksheets: Exponential Growth: Investing Worksheet (available at ttp://www.uen.org/Lessonplan/preview.cgi?LPid=24626) Exponential Decay: Car Depreciation