Section 7 Topic 1 Geometric Sequence How do
- Slides: 13
Section 7 Topic 1 Geometric Sequence
How do we tell if a sequence is a geometric sequence? • Each term in a sequence is the product of the previous term and some real number • 3, 6, 12, 24…
Arithmetic Sequences and Function notation Term Number Sequence Term 1 A 1 3 2 A 2 6 3 A 3 12 4 A 4 24 5 A 5 48 6 A 6 96 Function Notation F(1) A formula to find the 1 st term F(2) A formula to find the 2 nd term F(3) A formula to find the 3 rd term F(4) A formula to find the 4 th term F(n) A formula to find nth term
Find the term in the sequencestudents will fill this in during the lesson. Term Number Sequence Term 1 a 1 3 2 a 2 6 3 a 3 12 4 a 4 24 5 a 5 48 6 a 6 96 7 a 7 192
Section 7 Topic 2 Exponential Functions
Entrance Question: Where did we first see Exponential functions? • Put your answer in the chat box for class participation credit.
4 ways to see this • • Verbal descriptions Algebraic equations Numeric Tables Graphs
Verbal descriptions Linear Function words Exponential function words • Constant rate • Steady increase • Students: Put two words in the chat box that would lead you to believe that your function was a linear function? • What is the equation for this? • Gravity • Does not travel at a constant speed. • Falls • What type of equations would represent this? Place your answer in the chat box.
Equations Algebraic Exponential • Y=mx+b • F(x)=ax 2 +bx +c
Tables Algebraic – adding or subtract H F(h) 1 60 2 120 3 4 Exponential– Multiply or Divide t 0 B(t) 100 180 1 2 200 400 240 3 800
How do you write an algebraic equation for exponential growth based on a table? Verbal model • You are performing an experiment in science class in which you start with 100 bacteria and the amount of bacterial doubles every hour. Exponential t 0 B(t) 100 1 2 200 400 3 800
Steps to the Equations • First Pick two points. One at the y-intercept and the other with a 1 for the x-axis • Second make two equations • Solution Fill in the numbers and solve
(0, 100) and (1, 200) • Y=abx use this twice Y=abx 100=ab 0 200=ab 1 100=a 200=100 b 2=b Y=100(2)x