Exponential Growth Decay Applications that Apply to Me

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 = 8

Group investigation: x Y = 2 �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 -1 0 1 2 3 F(x) = 2 x 2 -1 = ½ 20 = 1 21 = 2 22 = 4 23 = 8

The Graph of y = x 2

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. �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 Year 2: $110 + 110·(. 10) = $121 Year 3: $121 + 121·(. 10) = $133. 10 Year 4: $133. 10 + 133. 10·(. 10) = $146. 41 Year 5: $146. 41 + 1461. 41·(. 10) = $161. 05

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

Using the Equation �$100. 00 � 10% interest � 5 years � 100(1+ 100·(. 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

Which Investment? �The first one yields more money. �Choice 1: $16, 190. 94 �Choice 2: $15, 071. 10

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 10% Value after 2 Value after 5 Value after 8 Value after years 10 years $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