Math 8C Exponential Relationships Standards: Model exponential functions using tables, graphs, and equations, and translate between the three. Given a context, determine the growth/decay factor and rates. Use both recursive and explicit equations to notate exponential functions given a context. Identify key features of an exponential function. Use function notation to explain the relationship between domain and range. Translate exponential functions, f(x), vertically by adding a constant, f(x)+k. Compare exponential and linear functions showing that exponential functions are multiplicative and linear functions are additive: Differences on tables, shape of graphs, and structure of equations.

Given a context, determine the growth/decay factor and rates. Math 8C Day 1 Standards: Given a context, determine the growth/decay factor and rates. Identify key features of an exponential function: y-intercept, end behavior, and rate of change

Warm Up Find the next three terms in the sequence 3, 6, 12, 24, 48, … Rewrite the expression 3∙3∙3∙3∙3 using exponents. Rewrite the expression 5∙2∙2∙2 using exponents. 96, 192, 384 3 5 5∙ 2 3

Must Do (2/23): 1 3 9 27 81 2187 3,486,784,401

One Grain of Rice by Demi

One Grain of Rice by Demi

One Grain of Rice by Demi Now, Complete parts 1 – 3 on your handout. Fill in the spreadsheet based upon this story to determine the amount of rice given to Rani an any given day.

One Grain of Rice by Demi

One Grain of Rice by Demi

One Grain of Rice by Demi Complete parts 4 & 5 on your handout on your own. Complete parts 6 & 7 with your table group. Discuss how you should construct your equations. Be sure to run lots of tests!

Must Do (2/24): If offered, would you rather take a penny that doubles in value everyday for 30 days or a million dollars now? Day 1: $.01 Day 2: $.02 Day 3: $.04 Day 4: $.08 Day 5: $.16 Day 6: $.32 Day 7: $.64 Day 8: $1.28 Day 9: $2.56 Day 10: $5.12 Day 11: $10.24 Day 12: $20.48 Day 13: $40.96 Day 14: $81.92 Day 15: $163.84 Day 16: $327.68 Day 17: $655.36 Day 18: $1,310.72 Day 19: $2,621.44 Day 20: $5,242.88 Day 21: $10,485.76 Day 22: $20,971.52 Day 23: $41,943.04 Day 24: $83,386.08 Day 25: $167,772.16 Day 26: $335,544.32 Day 27: $671,088.64 Day 28: $1,342,177.28 Day 29: $2,684,354.56 Day 30: $5,368,709.12 Grand Total: $10,737,418.23

Alice in Wonderland

Alice in Wonderland

In Class Practice U5D11 – ICP (Graphing Alice)

Exponential Relationships These patterns of change show exponential growth. This is when the growth in a situation is multiplicative, rather than additive. Multiplicative growth is when you multiply by a constant number to get the next value in a table or graph. (Linear relationships are additive) The fixed number you multiply by is called the growth factor

Make a Table & Graph When you were born, your grandparents put $5 in a bank account for your college fund. Every birthday since, they have doubled the amount they put in from the previous year, but had to stop after 10 years. Why do you think they had to stop? Year Amount Deposited

Extension Trouble with Tribbles Video You Tube: trouble with tribbles spock http://www.youtube.com/watch?v=Bprgl_4z6gY Worksheet: http://mathbits.com/MathBits/MathMovies/TroubleTribblesWorksheet1.pdf